Chapter 03

Fi nanc i alManag e me nt :Cor eConc e pt s , 3 e ( Br ooks ) Chapter 3 The Time Time Value Value of of Money (Part 1)

3.1 Future Value and Compounding Interest Interest 1 )Yourg r a n dmo t he rp l a c e s$ 1 3 , 0 0 0i nt oa na c c o unte a r n i nga ni nt e r e s tr a t eof7 % pe ry e a r .Af t e r5y e a r s t hea c c o untwi l lbev al ue da t$ 18 , 2 33 . 1 7. Whi c hoft hef ol l o wi wi ngs t a t e me me nt si sc or r e c t ? A)Thepr e s e ntva l uei s$ 1 3, 0 00 ,t het i mepe r i odi s7ye a r s , t hepr e s e ntva l uei s$ 1 8, 2 3 3. 1 7 ,a ndt hei nt e r e s t r a t ei s5 %. %. B)Thef ut ur eva l uei s$ 13 , 0 00 ,t het i mepe r i odi s5ye ar s ,t hepr i nc i pa li s$ 18 , 2 33 . 1 7,a ndt hei nt e r e s tr a t ei s 7%. C)Thepr i nc i pa li s$ 1 3, 0 00 ,t het i mepe r i odi s5ye a r s ,t hef ut ur ev al uei s$ 1 8, 2 33 . 1 7,a ndt hei nt e r e s tr a t e i s7%. %. D)Thepr i nc i pa li s$ 1 3, 0 00 ,t het i mepe r i odi s7ye ar s ,t hef ut ur ev al uei s$ 18 , 2 33 . 1 7,a ndt hei nt e r e s tr a t e i s5%. %. Answer :C Ex pl a na t i on:C)The$ 13 , 0 00i st hepr i nc i pa lorpr e s e ntva l ue ,t hei nt e r e s tr a t ei ss t a t e da s7 %, %,t het i me pe r i odi si de nt i fie da s5ye a r s , a ndt hef ut ur ev a l uei s$ 1 8, 2 33 . 1 7. Di ff:2 T o pi c :3 . 1F ut ur eV a l uea n dCo mp mpo undi n gI n t e r e s t AACS B:3An a l y t i c a lThi n ki n g LO:3 . 1Ca l c u l a t ef ut ur ev a l ue sa n dunde r s t a ndc o mp mpo undi ng .

2 )Theo ne t i mepa y me me nto fmo ne ya taf ut ur eda t ei so f t e nc a l l e da_ _ _ _ _ __ _ . A)l ump mps um pa yme me nt B)pr e s e n tv a l ue C)pr i nci palamo mount D)per pet ui t ypayme ment Answer :A Di ff:1 T o pi c :3 . 1F ut ur eV a l uea n dCo mp mpo undi n gI n t e r e s t AACS B:3An a l y t i c a lThi n ki n g LO:3 . 1Ca l c u l a t ef ut ur ev a l ue sa n dunde r s t a ndc o mp mpo undi ng .

1 Co py r i g ht©2 0 1 6Pe a r s o nEduc a t i o n,I nc .

3 )A$ 1 0 0de po s i tt o da yt ha te a r nsa na nnua li nt e r e s tr a t eo f1 0 %i swo r t hho w muc ha tt hee n do ft wo y e ar s ?As s umea l li nt e r e s tr e c e i v eda tt hee ndoft hefir s ty ea ri sr e i nv es t e dt hes e c o ndy ea r . A)$10 0 B)$ 1 2 0 C)$121 D)$12 2 Answer :C n 2=$ 1 21 . 0 0 Expl anat i on:C)FV=PV∗ ( 1+r ) =$10 0∗ ( 1 . 10) MOD DE E=END I NPUT 2 10 KEY N I /Y CPT 121 . 00

100 PV

0 PMT

? FV

Di ff:2 T o pi c :3 . 1F ut ur eV a l uea n dCo mp mpo undi n gI n t e r e s t AACS B:3An a l y t i c a lThi n ki n g LO:3 . 1Ca l c u l a t ef ut ur ev a l ue sa n dunde r s t a ndc o mp mpo undi ng .

4 )Ani n ve s t me ntof$ 1 0 0t o da yi swo r t h$ 1 16 . 6 4att hee ndo ft woy e a r si fi te a r n sa na nnua li nt e r e s tr a t e of8%. %.How muchi nt er es ti se ar nedi nt hefir s tyearandhow muchi nt hesec ondyearoft hi si nvest ment ? A)Thei nt e r e s te a r n e di ny e a ronei s$ 8 . 3 2a ndt hei nt e r e s te a r n e di ny e a rt woi s$ 8 . 3 2 . B)Thei nt e r e s te a r ne di ny ea ro nei s$ 8 . 0 0andt hei nt e r e s te a r ne di ny e art woi s$ 8 . 6 4. C)Thei nt e r e s te a r ne di ny e aronei s$ 8 . 6 4andt hei nt e r e s te a r ne di ny ea rt woi s$ 8 . 0 0. D)The r ei sn ote no ug hi nf o r ma ma t i o nt os o l v et hi sp r o bl e m. m. Answer :B n 1 Expl anat i on:B)FV=PV∗ ( 1+r ) =$10 0∗ ( 1 . 08) -$ 1 0 0=$ 8 . 0 0a nd 1 8 . 6 4 $ 1 0 8 ( 1 . 0 8 ) -$ 1 0 8=$ Di ff:3 T o pi c :3 . 1F ut ur eV a l uea n dCo mp mpo undi n gI n t e r e s t AACS B:3An a l y t i c a lThi n ki n g LO:3 . 1Ca l c u l a t ef ut ur ev a l ue sa n dunde r s t a ndc o mp mpo undi ng .

5 )_ _ __ _ _ __i ss i mpl yt hei nt e r e s te a r n edi ns u bs e q ue ntpe r i o dso nt hei nt e r e s te a r n e di npr i o rpe r i o ds . A)Quo t e di nt e r e s t B)Ant i c i pa t e di nt e r e s t C)S i mpl ei nt e r e s t D)Comp mpoundi nt er es t Answer :D Di ff:1 T o pi c :3 . 1F ut ur eV a l uea n dCo mp mpo undi n gI n t e r e s t AACS B:3An a l y t i c a lThi n ki n g LO:3 . 1Ca l c u l a t ef ut ur ev a l ue sa n dunde r s t a ndc o mp mpo undi ng .


3 )A$ 1 0 0de po s i tt o da yt ha te a r nsa na nnua li nt e r e s tr a t eo f1 0 %i swo r t hho w muc ha tt hee n do ft wo y e ar s ?As s umea l li nt e r e s tr e c e i v eda tt hee ndoft hefir s ty ea ri sr e i nv es t e dt hes e c o ndy ea r . A)$10 0 B)$ 1 2 0 C)$121 D)$12 2 Answer :C n 2=$ 1 21 . 0 0 Expl anat i on:C)FV=PV∗ ( 1+r ) =$10 0∗ ( 1 . 10) MOD DE E=END I NPUT 2 10 KEY N I /Y CPT 121 . 00

100 PV

0 PMT

? FV


4 )Ani n ve s t me ntof$ 1 0 0t o da yi swo r t h$ 1 16 . 6 4att hee ndo ft woy e a r si fi te a r n sa na nnua li nt e r e s tr a t e of8%. %.How muchi nt er es ti se ar nedi nt hefir s tyearandhow muchi nt hesec ondyearoft hi si nvest ment ? A)Thei nt e r e s te a r n e di ny e a ronei s$ 8 . 3 2a ndt hei nt e r e s te a r n e di ny e a rt woi s$ 8 . 3 2 . B)Thei nt e r e s te a r ne di ny ea ro nei s$ 8 . 0 0andt hei nt e r e s te a r ne di ny e art woi s$ 8 . 6 4. C)Thei nt e r e s te a r ne di ny e aronei s$ 8 . 6 4andt hei nt e r e s te a r ne di ny ea rt woi s$ 8 . 0 0. D)The r ei sn ote no ug hi nf o r ma ma t i o nt os o l v et hi sp r o bl e m. m. Answer :B n 1 Expl anat i on:B)FV=PV∗ ( 1+r ) =$10 0∗ ( 1 . 08) -$ 1 0 0=$ 8 . 0 0a nd 1 8 . 6 4 $ 1 0 8 ( 1 . 0 8 ) -$ 1 0 8=$ Di ff:3 T o pi c :3 . 1F ut ur eV a l uea n dCo mp mpo undi n gI n t e r e s t AACS B:3An a l y t i c a lThi n ki n g LO:3 . 1Ca l c u l a t ef ut ur ev a l ue sa n dunde r s t a ndc o mp mpo undi ng .

5 )_ _ __ _ _ __i ss i mpl yt hei nt e r e s te a r n edi ns u bs e q ue ntpe r i o dso nt hei nt e r e s te a r n e di npr i o rpe r i o ds . A)Quo t e di nt e r e s t B)Ant i c i pa t e di nt e r e s t C)S i mpl ei nt e r e s t D)Comp mpoundi nt er es t Answer :D Di ff:1 T o pi c :3 . 1F ut ur eV a l uea n dCo mp mpo undi n gI n t e r e s t AACS B:3An a l y t i c a lThi n ki n g LO:3 . 1Ca l c u l a t ef ut ur ev a l ue sa n dunde r s t a ndc o mp mpo undi ng .


6 )Whi c hoft hef ol l o wi wi ngi st hec or r e c tf or mu mul af orc a l c ul a t i ngt hef ut ur ev a l ue ? A)FV= n B)FV=PV×( 1+r ) n C)PV=FV×( 1+r ) D)PV=

-1

Answer :B Di ff:2 T o pi c :3 . 1F ut ur eV a l uea n dCo mp mpo undi n gI n t e r e s t AACS B:3An a l y t i c a lThi n ki n g LO:3 . 1Ca l c u l a t ef ut ur ev a l ue sa n dunde r s t a ndc o mp mpo undi ng .

7 )Whi c hoft hef o l l o wi wi ngwi l lr e s ul ti naf ut ur ev a l uegr e a t e rt ha n$ 1 00 ? A)PV =$50 ,r =a na nnua li nt e r e s tr a t eo f1 0 %, %,a ndn =8y e a r s . B)PV=$75, =a na nnua li nt e r e s tr a t eof1 2 %, %,a ndn =3y e a r s . r C)PV=$90 ,r =a na nnua li nt e r e s tr a t eo f1 4 %, %,a ndn =1y e a r . D)Al lo ft hef ut ur ev a l ue sa r egr e a t e rt ha n$ 1 00 . Answer :D n 8=$ Expl anat i on:D)FV=PV∗ ( 1+r ) =$50∗ ( 1 . 10) 1 0 7 . 1 8 3=$1 05 . 3 7 $75∗ ( 1 . 12 ) 1=$ $90∗ ( 1 . 14 ) 10 2. 6 0 Di ff:3 T o pi c :3 . 1F ut ur eV a l uea n dCo mp mpo undi n gI n t e r e s t AACS B:3An a l y t i c a lThi n ki n g LO:3 . 1Ca l c u l a t ef ut ur ev a l ue sa n dunde r s t a ndc o mp mpo undi ng . Hmwr kQu Que s t i o ns :*T a k e nf r o m" Pr e ppi ngf o rE x am ms s "q ue s t i o nsa tt h ee ndo ft h ec h ap t e r .

8 )At wo y e a ri n ve s t me nto f$ 2 0 0i sma ma det o da ya ta na nnua li nt e r e s tr a t eof6 %. %.Whi c hoft hef o l l o wi wi ng s t a t e me me nt si st r ue ? A)ThePVi Vi s$1 78 . 0 0. B)TheF Vi s$ 2 2 4 . 0 0 . C)TheFVi s$224. 72. D)Thi sq ue s t i o ni si r r e l e v antbe c a us et he r ea r en ot woy e ari n ve s t me nt st ha te a r nana v e r a g eof6 % pe r y e a r . Answer :C n 2=$ 2 24 . 7 2 Expl anat i on:C)FV=PV∗ ( 1+r ) =$20 0∗ ( 1 . 06) MOD DE E=END I NPUT 2 6 KEY N I /Y CPT 224 . 72

200 PV

0 PMT

? FV



9 )At wo y e a ri n ve s t me nto f$ 2 0 0i sma ma det o da ya ta na nnua li nt e r e s tr a t eof6 %. %.Whi c hoft hef o l l o wi wi ng s t a t e me me nt si st r ue ? A)Thei nt e r e s te a r n e di ny e a rt woi s$ 1 2 . 0 0andy e a ro nei s$ 1 2 . 7 2 . B)Thei nt e r e s te a r n edi ny e aro nei s$ 1 2 . 0 0andy e art woi s$ 1 2 . 7 2 . C)TheFVi s$224. 00. D)Thef ut ur ev a l uewo wo ul db egr e a t e ri ft hei nt e r e s tr a t ewe we r el o we we r . Answer :B n 1 Expl anat i on:B)FV=PV* ( 1+r ) =$ 2 00 * ( 1 . 0 6) =$ 2 1 2a nd$ 2 1 2-$ 2 0 0=$ 1 2=i nt e r e s te a r n e di ny e a r 1 one .$ 21 2* ( 1 . 0 6) =$ 2 2 4 . 7 2a nd$ 2 2 4 . 7 2-$ 2 1 2=$ 12 . 7 2 =i nt e r e s te a r n edi ny e a rt wo . Di ff:2 T o pi c :3 . 1F ut ur eV a l uea n dCo mp mpo undi n gI n t e r e s t AACS B:3An a l y t i c a lThi n ki n g LO:3 . 1Ca l c u l a t ef ut ur ev a l ue sa n dunde r s t a ndc o mp mpo undi ng .

1 0 )At wo y e a ri n ve s t me nto f$ 3 5 0 0i sma ma det o da yata na nnua li nt e r e s tr a t eof5 . 7 5 %. %.Whi c ho ft he f ol l o wi wi ngs t a t e me me nt si st r ue ? A)Thef ut ur ev a l uewo woul db egr e a t e ri ft hei nt e r e s tr a t ewa wa shi ghe r . B)Thepr e s e n tv a l uewo woul db egr e a t e ri ft hei nt e r e s tr a t ewa wa shi ghe r . C)Thef ut ur eva l uewo woul db egr e a t e ri ft hei nt e r e s tr a t ewa wa sl o we we r . D)Thef ut ur ev a l uedoe sn otc h ang east hei nt e r e s tr a t ec h ang e s . Answer :A Di ff:2 T o pi c :3 . 1F ut ur eV a l uea n dCo mp mpo undi n gI n t e r e s t AACS B:3An a l y t i c a lThi n ki n g LO:3 . 1Ca l c u l a t ef ut ur ev a l ue sa n dunde r s t a ndc o mp mpo undi ng .

1 1)I nt woy e ar sBor i spl a nst oe nr o l la tCl e e s eUni v er s i t y , apr e s t i gi ousuni v er s i t yi nt hePa c i ficNor t hwe s t oft heUS US A.I ft hec ur r e ntt ui t i oni s$ 2 3, 5 00pe ry e a ra ndi se x pe c t e dt oi nc r e a s eatar a t eof6 % pe ry e a r , ho w muc hwi l lBo r i spa yi nt ui t i onhi sfir s ty e a rofs c ho ol ?( Hi sfir s tt ui t i o npa y me me nti se x a c t l yt woy e ar s f r o mt o da y . )I nhi sf our t hy e a r ?( Hi sl a s tt ui t i onpa y me me nti se x a c t l y5ye a r sf r o mt o da y )( Ro unde dt ot he ne ar e s tdol l a r . ) A)$ 2 3 , 5 0 0a nd$ 2 9 , 6 6 8 B)$ 2 6, 4 0 5and$ 2 9, 6 6 8 C)$ 2 3 , 5 0 0a nd$ 3 1 , 4 4 8 D)$ 2 6 , 4 0 5a nd$ 3 1 , 4 4 8 Answer :D n 2=$ 5=$ Expl anat i on:D)FV=PV* ( 1+r ) =$ 2 3 , 5 0 0∗ ( 1 . 06) 2 6 , 4 05a nd$ 2 3 , 5 0 0∗ ( 1 . 0 6) 31 , 4 48 MOD DE E=END I NPUT 2 KEY N CPT 26, 4 05 MOD DE E=END I NPUT 5 KEY N CPT 31, 4 48

6 I /Y

23, 500 0 PV PMT

? FV

6 I /Y

23, 500 0 PV PMT

? FV

Di ff:3 T o pi c :3 . 1F ut ur eV a l uea n dCo mp mpo undi n gI n t e r e s t AACS B:3An a l y t i c a lThi n ki n g 4 Co py r i g ht©2 0 1 6Pe a r s o nEduc a t i o n,I nc .

LO:3 . 1Ca l c u l a t ef ut ur ev a l ue sa n dunde r s t a ndc o mpo undi ng .

12)Andywoul dl i ket obuyanew c arbutmus tc ompl et eat woyearc ommi t mentt ot hePeaceCor p be f or ehewi l ldr i vet hene wc ar .Thec ur r e ntpr i c eoft hec arAndywant st obuyi s$2 2, 0 00,andt hede al e r e x pe c t st hepr i c eo fas i mi l a rne wc a rt obe$ 24 , 0 0 0i nt woy e ar s . I fAndyc a ne a r na na nnua li nt e r e s tr a t e of3% onhi smoney ,s houl dhebuyt hecarnow orwai tf ort woyear s ?Why?Not e: St oragecos t si fAndy pur c ha s e st hec a ra r e$ 0 .Pl e a s el i mi ty ourc o ns i de r a t i onst ot h ef a c t or soffe r e di nt hea ns we rc hoi c e s . A)Buyno w be c a us ei fAndyi n ve s t st he$ 22 , 0 0 0t o da yi twi l lonl yi nc r e a s ei nv al uet o$ 2 3, 3 4 0 ,a ndt hi si s l e s st ha nt hec o s tofhi sde s i r e dne wc a ri nt woy e ar s . B)Andyi si ndi ffe r e ntbe c a us ehi s$ 2 2 , 0 0 0i n ve s t me ntwi l lbewo r t he x a c t l y$ 2 4, 0 0 0a f t e rt woy e a r s . C)Buyi nt woye a r sb e c a us ea t$ 2 4 , 0 0 0t hec a rwi l lc o s tl e s st ha nt he$ 2 4, 3 8 5Andywi l lha v eaf t e r i n ve s t i ngt hemo ne yf o rt woye a r s . D)Buyi nt woye a r sb e c a u s e$ 2 4 , 0 0 0i sar e a lde a lf o rt hec a rAndywa nt s . Answer :A n 2=$ Expl anat i on:A)FV=PV* ( 1+r ) =$ 22 , 0 00 * ( 1 . 0 3) 2 3 , 3 4 0 MODE=END I NPUT 2 3 KEY N I /Y CPT 23, 3 40

22, 000 0 PV PMT

? FV

Di ff:3 T o pi c :3 . 1F ut ur eV a l uea n dCo mpo undi n gI n t e r e s t AACS B:3An a l y t i c a lThi n ki n g LO:3 . 1Ca l c u l a t ef ut ur ev a l ue sa n dunde r s t a ndc o mpo undi ng .

1 3 )Ol i vi aa ndhe rs po us eh a v es a v e d$ 4 , 5 0 0f o ra1 2 da yc r u i s ev a c a t i o ni nEur o pe . Thec o upl ene e ds $ 5, 0 00f ora" n i c e "c a bi nor$ 6 , 0 00f ora" l ux ur y "c a bi n.I fc a bi npr i c e sa r ee xpe c t e dt or e ma i nc o ns t a ntf or t hene x tt hr e ey e a r sa ndOl i vi ae xpe c t st oe a r n6 % pe ry e a ro nhe ri n ve s t me nt s , wi l lt hec o upl e ' ss a v i ngs bee nought oaffor dt he" ni c e "c abi ni nt hr e eye a r s ?Cant he yaffor dt hel uxur yc abi n?Whyorwhynot ? A)Ye s , t he yc a na ffo r dt he" n i c e "c a b i no rt hel ux ur yc a bi nbe c a us et he i r$ 4 , 5 0 0i n ve s t me ntwi l li nc r e a s e t o$ 6 , 3 6 0b yt hee ndofy e a rt hr e e . B)Ye s , t he yc ana ffor dt he" ni c e "c a bi nort hel ux ur yc a bi nbe c a us et he i r$ 4, 5 00i nv es t me ntwi l li nc r e a s et o $ 5 , 3 6 0byt hee ndo fy e a rt hr e e . C)Ye s , t he yc a na ffo r dt he" ni c e "c a b i nb utNOTt hel ux ur yc a b i nb e c a us et he i r$ 4 , 5 0 0i n ve s t me ntwi l l onl yi nc r e a s et o$ 5, 3 60byt hee ndofy ea rt hr e e . D)No ,t he yc a nno ta ffor dt he" ni c e "c a b i nort hel ux ur yc a b i nbe c a us et he i r$ 4 , 5 0 0i n ve s t me ntwi l lonl y i nc r e a s et o$ 4 , 9 5 0b yt hee ndo fy e a rt hr e e . Answer :C n 3=$ 5 , 3 6 0 Expl anat i on:C)FV=PV∗ ( 1+r ) =$ 4 , 5 0 0∗ ( 1 . 06) MODE=END I NPUT 3 6 KEY N I /Y CPT 5, 36 0

4, 5 00 PV

0 ? PMT FV



1 4 )Aho mei mpr o ve me ntfir m ha sq uo t e dapr i c eo f$ 9 , 8 0 0t ofixupEr i c ' sb a c ky a r d .F i v ey e a r sa g o,Er i c put$7, 500i nt oahomei mpr ovementacc ountt hathase ar nedanaver ageof5. 25% peryear .DoesEr i chave enoughmoneyi nhi sacc ountt opayf ort hebackyar dfixup? A)Yes ;Er i cnow hasexact l y$9, 800i nhi shomei mpr ovementacc ount . B)No;Er i chasonl y$9, 687i nhi shomei mpr ovementacc ount . C)Yes; Er i cnow has$10, 519i nhi shomei mpr ovementacc ount . D)The r ei sn ote no ug hi nf o r ma t i o nt oa ns we rt hi sq ue s t i o n. Answer :B n 5=$ Expl anat i on:B)FV=PV∗ ( 1+r ) =$ 7 , 5 0 0∗ ( 1 . 0 52 5) 9, 6 87 MODE=END I NPUT 5 5. 25 KEY N I /Y CPT 9, 68 7

7, 5 00 PV

0 PMT

? FV

Di ff:3 T o pi c :3 . 1F ut ur eV a l uea n dCo mpo undi n gI n t e r e s t AACS B:3An a l y t i c a lThi n ki n g LO:3 . 1Ca l c u l a t ef ut ur ev a l ue sa n dunde r s t a ndc o mpo undi ng . Hmwr kQue s t i o ns :*T a k e nf r o m" Pr e ppi ngf o rE x a ms "q ue s t i o nsa tt h ee ndo ft h ec h ap t e r .

1 5 )Whi c hoft hef o l l o wi ngi n ve s t me nt sh asal a r g e rf ut ur ev a l ue :A$ 1 0 0i n ve s t me nte a r n i ng1 0 % pe ry e a r f o r5y e a r sora$ 1 00i n ve s t me nte a r n i ng5% pe ry e arf or1 0y e ar s ? A)Ani n ve s t me ntof$ 1 00i n ve s t e da t1 0 % pe ry e a rf or5y e ar sbe c a us ei tha saf ut ur ev al ueof$ 1 61 . 0 5 . B)Ani n ve s t me nto f$ 1 0 0i n ve s t e da t1 0 % pe ry e arf o r5y e ar sb e c a us ei tha saf ut ur ev al ueof$ 1 6 2. 8 9 . C)Ani n ve s t me nto f$ 1 00i n ve s t e da t5 % pe ry e a rf or1 0ye a r sb ec a us ei tha saf ut ur ev a l ueof$ 1 6 1. 0 5 . D)Ani n ve s t me ntof$ 1 00i n ve s t e da t5 % pe ry e arf o r1 0y ea r sbe c a us ei tha saf ut ur ev al ueof$ 1 62 . 8 9 . Answer :D n 5 10=$ Expl anat i on:D)FV=PV∗ ( 1+r ) =$10 0∗ ( 1 . 10) =$161. 05and$100∗ ( 1 . 05) 1 6 2 . 8 9 MODE=END I NPUT 5 KEY N CPT 161. 05 MODE=END I NPUT 10 KEY N CPT 162. 89

10 I /Y

100 PV

0 PMT

? FV

5 I /Y

100 PV

0 PMT

? FV



1 6 )Whi c hoft hef o l l o wi ngi n ve s t me nt sha sal a r g e rf ut ur ev a l ue :I n ve s t me ntA,a$ 1, 0 0 0i n ve s t me nt e a r n i ng5% pe ry e a rf or6y e ar s , o rI n ve s t me ntB,a$ 5 0 0i n ve s t me nte a r n i ng10 % pe ry e a rf o r6y e a r s ,wi t h abo nuso fa ne x t r a$ 5 0 0a dde da tt hee ndo ft hes i x t hy e a r ? A)I n ve s t me ntB,wi t haf ut ur ev al ueo f$ 1 , 3 8 6. B)I n ve s t me ntA,wi t haf ut ur ev al ueo f$ 1 , 3 8 6. C)I n ve s t me ntA,wi t haf ut ur ev a l ueo f$ 1 , 3 4 0. D)Thei nvest ment shaveequalval ue. Answer :A n 6 Expl anat i on:A)I nves t mentA:FV=PV ∗ ( 1+r ) =$ 1 , 0 0 0∗ ( 1 . 05) =$ 1, 3 40 . n 6 I nves t mentB:FV=PV ∗ ( 1+r ) =$500∗ ( 1 . 1 0) +$ 5 00=$ 1 , 3 8 6.Thef ut ur ev al ueo fI n ve s t me ntBi s l a r g e rt ha nt hef ut ur ev al ueofI n ve s t me ntAb y$ 4 6 . Di ff:3 T o pi c :3 . 1F ut ur eV a l uea n dCo mpo undi n gI n t e r e s t AACS B:3An a l y t i c a lThi n ki n g LO:3 . 1Ca l c u l a t ef ut ur ev a l ue sa n dunde r s t a ndc o mpo undi ng .

17)Youwi s ht omakeasubs t ant i aldownpaymentonal akecot t ageandyoucurr ent l yhave$18, 325 i n ve s t e da ta na nnua lr a t eof4 . 7 5 %.Ho w muc hmo ne ywi l lb ei nt hea c c o unti n2 . 5ye a r si fi tc o nt i nue st o e ar na ti t spr e s e ntr a t e ? A)$ 1 8 , 3 2 5 B)$ 19 , 4 64 C)$ 2 0, 5 7 9 D)$ 2 0 , 6 0 5 Answer :C n 2. 5=$ Expl anat i on:C)FV=PV∗ ( 1+r ) =$ 1 8 , 3 2 5∗ ( 1 . 0 47 5) 2 0 , 5 7 9 MODE=END I NPUT 2. 5 4. 75 KEY N I /Y CPT 20, 5 79

18, 325 0 PV PMT

? FV


1 8 )I fy oui n ve s t$ 3 , 6 5 0t o da y , ho w muc hmo ne ywi l ly ouha v ei n4y e a r s ? A)$ 3 , 6 5 0 B)$ 4, 4 37 C)Thi sq ue s t i o nc a n no tb ea ns we r e db e c a us ei ti smi s s i nga na nnua lr a t eofr e t ur n. D)Thi sq ue s t i o nc a n no tb ea ns we r e db e c a us ei ti smi s s i ngt het y peo fi n ve s t me ntma de . Answer :C Di ff:1 T o pi c :3 . 1F ut ur eV a l uea n dCo mpo undi n gI n t e r e s t AACS B:3An a l y t i c a lThi n ki n g LO:3 . 1Ca l c u l a t ef ut ur ev a l ue sa n dunde r s t a ndc o mpo undi ng .


1 9 )Thec ur r e n tpr i c eo na6 0 i nc hfla tpa ne lLCDHDt e l e vi s i o ni s$ 2 , 3 0 0 .Bi gs c r e e nHDt e l e vi s i onpr i c e s ha v edr o ppe da ta na v e r a g er a t eo f9 % pe ry e a ri nr e c e nty e ar s . I fy oue x pe c tt hi st r e ndt oc ont i nue ,ho w muc hwi l lt hi ss t yl eoft e l e vi s i onc os ti nt hr e eye ar s ? A)$ 2 , 9 7 9 B)$ 2, 3 00 C)$ 1 , 9 5 8 D)$ 1 , 7 3 3 Answer :D 3=$ Ex pl a na t i o n:D)Ex pe c t e df ut ur eva l ueoft e l e vi s i on=$ 2 , 3 0 0∗ ( 1-0. 0 9) 1 , 7 3 3 . 2 1 MODE=END I NPUT 3 9 KEY N I /Y CPT 1, 73 3. 2 1

2, 3 00 PV

0 PMT

? FV


2 0 )Thefina nc i a la i do ffic ea ty ouru ni v e r s i t yha so ffe r e dt opa yyo urf ul la nnua lt ui t i onc o s tof$ 2 2, 0 0 0 t hi sy e ar ,a sl onga syouma i nt a i nagr a depoi nta v er a geof3 . 0 0.I ft ui t i onc o s t sr i s ea tar a t eof6 % pe ry e ar whi l ey oua r ei nc o l l e g e ,butt hefina nc i a la i do ffic ec o nt i nue st opa ye xa c t l y$ 2 2 , 0 0 0pe ry e a rf o ry our t ui t i on,ho w muc hout o f po c ke tt ui t i o nc o s t swi l ly ouha v ey ours e n i o ry e a r ?NOTE:Thi nkc a r e f ul l y a b outt hi sp r o b l e m whe nfig ur i ngt hen umb e ro fy e a r sf r o mt hes t a r to fy ourf r e s hma ny e a rt ot hes t a r to f y ours e n i o ry e a r ,a s s umi ngnor ma lpr ogr e s st o wa r dgr a dua t i oni nf o ury e ar s . F ur t he r ,b ea wa r et ha twhi l e t ui t i onc o s t sa r er i s i ngy ourt ui t i oni sc o v er e dupt oonl y$ 22 , 0 00 .Youmus tpa ya nye x c e s st ui t i onc o s t s . A)$0 B)$ 3, 3 51 C)$ 4 , 2 0 2 D)$ 5 , 7 7 4 Answer :C n 3 Expl anat i on:C)FV=PV∗ ( 1+r ) -PV=$22, 000∗ ( 1 . 06) -$ 22 , 0 00=$ 26 , 2 02-$ 2 2, 0 0 0=$ 4, 2 02 Di ff:3 T o pi c :3 . 1F ut ur eV a l uea n dCo mpo undi n gI n t e r e s t AACS B:3An a l y t i c a lThi n ki n g LO:3 . 1Ca l c u l a t ef ut ur ev a l ue sa n dunde r s t a ndc o mpo undi ng .

2 1 )Co ns i de rt heTVM e qua t i on:Ani nc r e a s ei nt hepr e s e n tv al uewi l lde c r e a s et hef ut ur ev al ue ,o t he r t hi ng sr e ma i ni nge q ua l . Ans we r :F ALSE Ex pl a na t i o n:Ani nc r e a s ei nt hepr e s e ntv a l uewi l lI NCREAS Et hef ut ur ev a l ue ,o t he rt hi ng sr e ma i ni ng e q u a l . Di ff:1 T o pi c :3 . 1F ut ur eV a l uea n dCo mpo undi n gI n t e r e s t AACS B:3An a l y t i c a lThi n ki n g LO:3 . 1Ca l c u l a t ef ut ur ev a l ue sa n dunde r s t a ndc o mpo undi ng .


2 2)Cons i de rat woy e ari nv es t me nt :Gi v enac ons t a nta ndpos i t i vei nt e r e s tr a t e ,t hei nt e r e s te a r ne di nt he s e c o ndy e a rwi l lb egr e a t e rt ha nt hei nt e r e s te a r ne di nt hefir s ty e a r( a s s umi nga nnua lc o mpo undi ng ) . Ans we r :TRUE Ex pl a na t i on:Thes e c o ndy ea re a r nsi nt e r e s tont hefir s ty ea ri nt e r e s ta swe l la si nt e r e s tont hepr i nc i pa l . Di ff:1 T o pi c :3 . 1F ut ur eV a l uea n dCo mpo undi n gI n t e r e s t AACS B:3An a l y t i c a lThi n ki n g LO:3 . 1Ca l c u l a t ef ut ur ev a l ue sa n dunde r s t a ndc o mpo undi ng .

2 3 )Co ns i de rt heTVM e qua t i on:Ade c r e a s ei nt hei nt e r e s tr a t ewi l lde c r e a s et hef ut ur eva l ue ,o t he rt hi ngs r emai ni ngequal . Ans we r :TRUE Di ff:1 T o pi c :3 . 1F ut ur eV a l uea n dCo mpo undi n gI n t e r e s t AACS B:3An a l y t i c a lThi n ki n g LO:3 . 1Ca l c u l a t ef ut ur ev a l ue sa n dunde r s t a ndc o mpo undi ng .

2 4 )Co ns i de rt heTVM e qua t i on:Ade c r e a s ei nt het i mepe r i o dwi l li nc r e a s et hef ut ur ev al ue ,o t he rt hi ngs r emai ni ngequal . Ans we r :F ALSE Ex pl a na t i o n:Ade c r e a s ei nt het i mep e r i o dwi l lDECREAS Et hef ut ur ev a l ue ,o t he rt hi ng sr e ma i ni ng e q u a l . Di ff:1 T o pi c :3 . 1F ut ur eV a l uea n dCo mpo undi n gI n t e r e s t AACS B:3An a l y t i c a lThi n ki n g LO:3 . 1Ca l c u l a t ef ut ur ev a l ue sa n dunde r s t a ndc o mpo undi ng .

2 5 )Co ns i de rt heTVM e qua t i on:Thef ut ur ev a l uei sa l wa y sgr e a t e rt ha nt hepr e s e ntv al ue ,e v e ni ft he i nt e r e s tr a t ei sne ga t i ve . Ans we r :F ALSE Ex pl a na t i on:Thef ut ur ev al uei sl e s st ha nt hepr e s e ntva l uei ft hei nt e r e s tr a t ei sne ga t i ve . Di ff:2 T o pi c :3 . 1F ut ur eV a l uea n dCo mpo undi n gI n t e r e s t AACS B:3An a l y t i c a lThi n ki n g LO:3 . 1Ca l c u l a t ef ut ur ev a l ue sa n dunde r s t a ndc o mpo undi ng .

n 26 )TheTVM equat i onFV=PV×( 1+r ) c a nb ea l g e br a i c a l l yma ni pul a t e dt os o l v ef o ra nyo ft he var i abl esEXCEPTf ort het i meper i odn. Ans we r :F ALSE Ex pl a na t i o n:TheTVM e qua t i onc a nbeus e dt os o l v ef o ra n yoft hev a r i a bl e s ; FV,PF ,r , o rn. Di ff:2 T o pi c :3 . 1F ut ur eV a l uea n dCo mpo undi n gI n t e r e s t AACS B:3An a l y t i c a lThi n ki n g LO:3 . 1Ca l c u l a t ef ut ur ev a l ue sa n dunde r s t a ndc o mpo undi ng .


2 7 )$ 1 0 0i n ve s t e da tar a t eo f5 %f o r1 0y ea r sha st hes a mef ut ur ev al uea s$ 1 0 0i n ve s t e da t1 0 % c ompoundedannual l yf or5yea r s . Ans we r :F ALSE 5=$ 10=$ Ex pl a na t i o n:$ 1 00∗ ( 1 . 10) 1 6 1 . 0 5 ,but$ 1 00∗ ( 1 . 05) 1 6 2 . 8 9 MODE=END I NPUT KEY CPT MODE=END I NPUT KEY CPT

5 10 N I /Y 16 1. 05

100 PV

0 ? PMT FV

10 5 N I /Y 16 2. 89

100 PV

0 ? PMT FV


2 8 )$ 5 , 0 0 0i n ve s t e da ta na nnua lr a t eof6 %f o r3y e ar sha sas ma l l e rf ut ur eva l uet ha n$ 5 , 0 0 0i n ve s t e da ta n a nnua lr a t eo f3 %f or6y e ar s . Ans we r :TRUE 3=$ 6=$ Ex pl a na t i on:$ 5, 0 00∗ ( 1 . 06) 5 , 9 5 5 . 0 8, but$ 5, 0 00∗ ( 1 . 03) 5 , 9 7 0 . 2 6 Di ff:2 T o pi c :3 . 1F ut ur eV a l uea n dCo mpo undi n gI n t e r e s t AACS B:3An a l y t i c a lThi n ki n g LO:3 . 1Ca l c u l a t ef ut ur ev a l ue sa n dunde r s t a ndc o mpo undi ng .

29)I fyourbankoffer sa5% annualr at eofr et ur ncompoundedannual l y, t henatt heendofoneyearyour $ 1 , 0 0 0 . 0 0de po s i two ul dg r o wb y$ 5 0 . 0 0t o$ 1 , 0 5 0 . 0 0 .Ho we v e r ,i nt hes e c o ndy e a r ,y ourd e po s i two ul d i nc r e a s eb y$ 5 2. 5 0 25t oat o t a le ndi ngv al ueof$ 1 , 1 0 2 . 5 0 .Ex pl a i nwh yt hes e c o ndy e are a r nsmo r ei nt e r e s t o nt hei n ve s t me ntt ha nt hefir s ty e a r . Ans we r :Thes t ude nts h oul dunde r s t a ndt ha ti nt hes e c o nda nds u bs e que nty e a r st hei n ve s t me nti s e ar ni ngi nt e r e s tont hei nt e r e s ta l r e a dye ar ne di nt heea r l i e rpe r i od,a swe l la si nt e r e s tont hei ni t i a l pr i nc i pa l .Thus , i ne a c hpe r i odt he$ 1, 0 0 0. 0 0i ni t i a li nv es t me nte a r ns$ 5 0 . 0 0andi nt hes e c o ndy ea rt he i nt e r e s te ar ne dont hei nt e r e s ti s( $ 50 . 0 0)∗ ( . 0 5)=$ 2. 5 0. Di ff:2 T o pi c :3 . 1F ut ur eV a l uea n dCo mpo undi n gI n t e r e s t AACSB:6Reflect i veThi nki ng LO:3 . 1Ca l c u l a t ef ut ur ev a l ue sa n dunde r s t a ndc o mpo undi ng .


3 0 )S a m wi s h e st oi n ve s t$ 8 , 0 0 0i nt oana c c o unte a r n i ng6 %c o mpo unde da nnua l l y . I fhei n ve s t st he mo ne yt o da y , ho w muc hwi l lb ei nt hea c c o unti n6y e a r s ?I fhewa i t st hr e ey e a r sb ef or ei n ve s t i nghi s $ 8, 0 00andi nv es t st ha tmone yf ort hr e ey e ar s ,wi l lhee ar none ha l foft hei nt e r e s te a r ne di nt hefir s t s c e na r i os i nc eh eha dt hes a mea mo unti n ve s t e da tt hes a mer a t ebutf o ro nl yo ne ha l fo ft het i me ? Expl ai nhow youar r i vedatyourans wer . n 6 Ans wer :FV=PV×( 1+r ) =$ 8 , 0 0 0×( 1 . 0 6 ) =$ 11 , 3 48 . 1 5,f orat ot a lof$ 3, 3 48 . 1 5i ni nt e r e s te ar ne d.The FVoft hes hor t e ri nv es t me nti sonl y$ 9 , 5 2 8. 1 3 ,f orat ot a lof$ 1 , 5 2 8. 1 3i nt e r e s te a r ne d—l e s st ha nha l foft he t o t a li nt e r e s te a r ne di nt hefir s ts c e na r i o.Thes t ude nts houl dr e c ogni z et ha tt hei nv es t ore a r nsl e s st ha n ha l foft hei nt e r e s tduet ot hes hor t e rc ompoundi ngpe r i o da ndl e s si nt e r e s tb ei nge a r n edo ni nt e r e s t . Di ff:3 T o pi c :3 . 1F ut ur eV a l uea n dCo mpo undi n gI n t e r e s t AACS B:3An a l y t i c a lThi n ki n g LO:3 . 1Ca l c u l a t ef ut ur ev a l ue sa n dunde r s t a ndc o mpo undi ng .

3.2 Present Value and Discounting 1 )Whi c hoft hef o l l o wi ngac t i o nswi l lI NCREAS Et hepr e s e ntv a l ueo fa ni n ve s t me nt ? A)De c r e a s et hei nt e r e s tr a t e . B)De c r e a s et hef ut ur ev al ue . C)I nc r e a s et hea mo unto ft i me . D)Al lo ft hea bo vewi l li nc r e a s et hepr e s e ntv al ue . Answer :A Expl anat i on:A)PV= Di ff:1 T opi c :3 . 2Pr e s e ntVa l uea ndDi s c o unt i ng AACS B:3An a l y t i c a lThi n ki n g LO:3 . 2Ca l c u l a t ep r e s e n tv a l ue sa ndunde r s t a nddi s c o unt i ng .

2)Whi choft hef ol l owi ngact i onswi l lDECREASEt hepr es entval ueofani nvest ment ? A)De c r e a s et hei nt e r e s tr a t e . B)De c r e a s et hef ut ur ev al ue . C)Dec r eas et heamountoft i me. D)Al lo ft hea bo vewi l lde c r e a s et hepr e s e n tv a l ue . Answer :B Expl anat i on:B)PV= Di ff:1 T opi c :3 . 2Pr e s e ntVa l uea ndDi s c o unt i ng AACS B:3An a l y t i c a lThi n ki n g LO:3 . 2Ca l c u l a t ep r e s e n tv a l ue sa ndunde r s t a nddi s c o unt i ng .


3 )Whi c hoft hef o l l o wi ngf o r mul a si sc o r r e c tf o rfindi ngt h epr e s e ntv al ueo fa ni n ve s t me nt ? A)FV= n B)PV=FV ×( 1+r ) C)PV=FVn ×( 1+r ) D)PV=FV× Answer :D Expl anat i on:D)PV= Di ff:1 T opi c :3 . 2Pr e s e ntVa l uea ndDi s c o unt i ng AACS B:3An a l y t i c a lThi n ki n g LO:3 . 2Ca l c u l a t ep r e s e n tv a l ue sa ndunde r s t a nddi s c o unt i ng .

4 )Y ouha v epur c h a s e daTr e a s u r ybo ndt ha twi l lpa y$ 1 0 , 0 0 0t oy ourn e wb or nc h i l di n1 5ye a r s . I ft hi s bondi sdi s c ount e da tar at eof3. 875% pe rye a r ,whati st oda y' spr i c e( pr e s e ntval ue )f ort hi sbond? A)$ 8 , 4 1 7 B)$ 8, 5 00 C)$ 5 , 6 5 4 D)$ 1 0 , 0 0 0 Answer :C Expl anat i on:C)PV= MODE=END I NPUT 15 KEY N CPT 5, 654

=

=$ 5, 6 54

3. 875 ? I /Y PV

0 PMT

10, 000 FV

Di ff:2 T opi c :3 . 2Pr e s e ntVa l uea ndDi s c o unt i ng AACS B:3An a l y t i c a lThi n ki n g LO:3 . 2Ca l c u l a t ep r e s e n tv a l ue sa ndunde r s t a nddi s c o unt i ng . Hmwr kQue s t i o ns :*T a k e nf r o m" Pr e ppi ngf o rE x a ms "q ue s t i o nsa tt h ee ndo ft h ec h ap t e r .


5 )Af ur n i t ur es t o r eha sas o f aons a l ef o r$ 3 99 . 0 0 ,wi t ht hepa yme ntdueoney e arf r om t o da y . Thes t or ei s wi l l i ngt odi s c o untt hepr i c ea ta na nnua lr a t eo f5 %i fy oupa yt o da y . Wha ti st hea mo unti fy oupa y today? A)$38 0 B)$ 3 9 9 C)$419 D)$39 4 Answer :A Expl anat i on:A)PV= MODE=END I NPUT 1 KEY N CPT 380

=

5 I /Y

=$ 3 80 . 0 0

? PV

0 PMT

3 99 FV

Di ff:2 T opi c :3 . 2Pr e s e ntVa l uea ndDi s c o unt i ng AACS B:3An a l y t i c a lThi n ki n g LO:3 . 2Ca l c u l a t ep r e s e n tv a l ue sa ndunde r s t a nddi s c o unt i ng .

6 )Y ouruni ve r s i t yi sr unni ngas pe c i a loffe ro nt ui t i on.Thi sy ea r ' st ui t i onc os ti s$ 18 , 0 00 .Ne xtye ar ' s t ui t i onc o s ti ss c h e dul e dt obe$1 9, 0 80 .Theuni v e r s i t yoffe r st odi s c o untne x ty e a r ' st ui t i ona tar a t eof6 % i fy oua gr e et opa ybot hy ea r s ' t ui t i oni nf ul lt oda y .Ho w muc hi st het o t a lt ui t i onbi l lt oda yi fy out a ket he offer? A)$ 1 8 , 0 0 0 B)$ 34 , 9 81 C)$ 3 7, 0 8 0 D)$ 3 6 , 0 0 0 Answer :D Ex pl a na t i o n:D)PV=

+t o da y ' st ui t i o n=

+$ 1 8 , 0 0 0=$ 3 6 , 0 0 0 . 0 0



7 )Ani n ve s t me ntpr o mi s e sap a y offo f$ 1 9 5t woa ndo ne ha l fy e a r sf r o mt o da y . Atadi s c o untr a t eo f7 . 5 % pe ry e a r ,wha ti st hepr e s e ntv al ueoft hi si nv es t me nt ? A)$ 1 6 2 . 0 3 B)$ 16 2. 7 5 C)$ 1 69 . 4 7 D)The r ei sn ote no ug hi nf o r ma t i o nt oa ns we rt hi sq ue s t i o n. Answer :B Expl anat i on:B)PV MODE=END I NPUT 2. 5 KEY N CPT 162 . 75

1 6 2 . 7 5 =$

=

7. 5 I /Y

? PV

0 PMT

195 FV


8 )Y ourp a r e n t sp l a nt os pe nd$ 2 0 , 0 0 0onac a rf o ry ouupo ngr a dua t i o nf r o mc o l l e g e .I fy ouwi l lgr a dua t e i nt hreeyear sandyourpar ent scanear n4. 125% annual l yont hei ri nvest ment ,how muchmoneymus t t he ys e ta s i det oda yf ory ourc a r ? A)$ 2 0 , 0 0 0 B)$ 17 , 7 04 C)$ 1 7, 7 1 6 D)$ 1 6 , 3 8 7 Answer :C Expl anat i on:C)PV=

1 7 , 7 1 5 . 9 7 =$

=

MODE=END I NPUT 3 4. 125 ? KEY N I /Y PV CPT 17 , 715 . 97

0 PMT

20, 000 FV



9)Youi nt endt obuyavacat i onhomei ns evenyearsandpl ant ohaves aved$50, 000f oradownpayment . How muc hmoneywoul dyouhavet opl ac et odayi nt oani nves t mentt hatear ns8% peryeart ohave enoughf oryourdes i r eddownpayment ? A)$ 2 9 , 1 7 5 B)$ 29 , 1 00 C)$ 3 7, 0 6 5 D)$ 2 5 , 0 0 0 Answer :A Expl anat i on:A)PV= MODE=END I NPUT 7 8 KEY N I /Y CPT 2 9, 17 4. 52

=

=$ 29 ,1 74 . 5 2

? PV

0 PMT

5 0, 00 0 FV


h 1 0)I nfiv eye a r sy ourol de s tc hi l dwi l lbei n8t g r a de ,a twhi c hpo i nty oua ndy ourf a mi l ypl a nt o v a c a t i o ni nEur o pe . Yo ue s t i ma t et ha ty ouwi l lne e d$ 2 0 , 0 0 0f o rt het r i p.Ho w muc hdoyo une e dt os e t a s i det o da yi fy ouc a npl a c ey o urmo ne yi na ni n ve s t me ntv e hi c l ee a r n i nga na v e r a g eof4 . 5 0 % pe ry e a r ? A)$ 1 4 , 9 6 1 B)$ 15 , 0 73 C)$ 1 6, 0 4 9 D)$ 1 6 , 0 5 8 Answer :C Expl anat i on:C)PV= MODE=END I NPUT 5 4. 5 KEY N I /Y CPT 1 6, 04 9. 02

=

=$ 1 6 , 0 4 9 . 0 2

? PV

0 PMT

2 0, 00 0 FV



1 1 )Yourg r a n dpa r e n t sl e a v eont he i rdr e a mv ac a t i ont oAnt a r c t i c ai nt woy e a r s . Thec r ui s ev a c a t i o nwi l l c o s tt he m$ 25 , 0 00 .I ft he yha v ea l r e a dys a v e d$ 2 3, 5 00anda r ei nv es t i ngi ta tar a t eof2 . 7 5 % pe ry e a r , wi l l t he yha v es a v e de no ug hmo ne yf o rt he i rt r i p? A)No ,b e c a us et he yf o r g o tt of a c t o ri nl o ngunde r we a re x pe ns e s . B)Yes, t ohaveenoughmoneyt heywoul dhaveal r eadyneededt osa ve$23, 375. C)Yes, t ohavee noughmoneyt heywoul dhaveal r eadyneededt osa ve$23, 680. D)No,t ohaveenoughmoneyt heywoul dhaveal r eadyneededt osa ve$23, 680. Answer :D Expl anat i on:D)PV= MODE=END I NPUT 2 2. 7 5 KEY N I /Y CPT 2 3, 67 9. 71

=

=$ 2 3 , 6 7 9 . 7 1

? PV

0 PMT

25, 000 FV


1 2 )T ode t e r mi net hepr e s e ntv a l ueo faf ut ur ea mo unt ,o nes ho ul d_ _ _ _ _ _ __t hef ut ur ec a s hflo ws . A)a nnui t i z e B)c ompound C)di s count D)mul t i pl y Answer :C Di ff:1 T opi c :3 . 2Pr e s e ntVa l uea ndDi s c o unt i ng AACSB:1Wr i t t enandOr alCommuni c at i on LO:3 . 2Ca l c u l a t ep r e s e n tv a l ue sa ndunde r s t a nddi s c o unt i ng . Hmwr kQue s t i o ns :*T a k e nf r o m" Pr e ppi ngf o rE x a ms "q ue s t i o nsa tt h ee ndo ft h ec h ap t e r .


1 3 )Thes c hoo ldi s t r i c tne e dst opa s sabondl e vyf orf undi ngt or e mo de le x i s t i ngs c ho ol sa n dt obui l dne w s c ho ol s . Ex pe ndi t ur e sf o rt hene wa ndr e mo de l e db ui l di ng swi l lb e gi n1 8mo nt hsa f t e rpa s s a g eoft he bond. I ft hes c hooldi s t r i c tr e c e i ve sal lf undi ngi mme di at e l yaf t e rt hepas s ageoft hebondandc ani nve s t t hef undsa tar a t eof3 . 7 5 % pe ry e a r ,ho wl a r g emus tt hebo ndb ef o rt hedi s t r i c tt oha v e$4 5 , 0 0 0, 0 0 0a tt he s t a r tofc ons t r uc t i on? A)$ 4 5 , 0 0 0 , 0 0 0 B)$ 4 7, 5 54 , 8 34 C)$ 42 , 5 56 , 3 97 D)$ 4 2 , 5 8 2 , 4 2 2 Answer :D Expl anat i on:D)PV=

4 2 , 5 8 2 , 4 2 1 . 6 2 =$

=

MODE=END I NPUT 1. 5 3. 75 KEY N I /Y CPT 42, 5 85, 4 21. 62

? PV

0 45, 000, 000 PMT FV


1 4 )Yourfi r m ha ss o l dafle e to f1 0 0c a r st oal o c a lfir ma tadi s c o unt e dpr i c eo f$ 2 0 , 0 0 0e a c h( at o t a lo f $ 2 , 0 0 0 , 0 0 0 )duei ns i xmont hs . Yo ua r ewi l l i ngt odi s c ountt hepur c h as epr i c ea ta na nnua lr a t eof4 %i ft he fir m payscas ht oday .Whati st hel eas tamountofmoneyyouwi l lacc epti ft hefir m paysyourcompany today? A)$ 2, 0 39 , 6 08 B)$ 1, 9 61 , 1 61 C)$ 1, 9 6 0, 4 9 5 D)Thi sp r o b l e mc a n no tb ea ns we r e db e c a us eweha v ea na nnua li nt e r e s tr a t eb uto nl yone ha l fy e a ri n t i me. Answer :B Expl anat i on:B)PV= MODE=END I NPUT . 5 4 KEY N I /Y CPT 1, 961, 161. 35

=

=$ 1 , 9 6 1 , 1 6 1 . 3 5

? PV

0 PMT

2, 000, 000 FV



1 5 )Y ourma nuf a c t ur i ngfir m ha sj us ts e c u r e das a l et ot hef e de r a lg ov e r n me ntwi t hpa y me nto f$ 4 5 0 , 0 0 0 duei nni nemo nt hs . Yo uha v ea s k e dy ourb ankf o rc a s ht o da ywi t ht hes t i pul a t i o nt ha ty ouwi l lg i v et he pr oceedsf r om t hegover nmentcont r actt ot hebanki nni nemont hs .Thebankhasagr eedt oyourr eques t i fyoual l ow t hem t odi s countt hecas hflowsa tanannualr at eof8%.How muchwi l lt hebankpayyou t odayundert hi sagr eement ? A)$ 4 2 4 , 7 6 1 B)$ 42 3, 8 89 C)$ 4 76 , 7 3 9 D)$ 4 5 0 , 0 0 0 Answer :A Expl anat i on:A)PV= MODE=END I NPUT . 75 KEY N CPT 424 , 76 1. 06

4 2 4 , 7 6 1 . 0 6 =$

=

8 I /Y

? PV

0 PMT

4 50, 0 00 FV


1 6 )Yourt r us tf undwi l lpa yyou$ 1 0 0, 0 0 0i ns i xy e ar swhe ny out ur n2 5 .As h a dyfina nc i a li ns t i t ut i onha s e nc o ur a g e dy out os i g na wa yt her i ght st oyo urt r us tf undi ne x c h a ng ef o rc a s ht o da y . Wo ul dy oupr e f e r t ha tt hefina nc i a li ns t i t ut i o nus eadi s c o untr a t eof8 %o r1 0 %t ode t e r mi net hev a l ueo fy o url umps u m pa yme nt ?Why? A)Us e8% becauset hel umps um paymentof$62, 741i sgreat ert hant he10% di s count edval ueof$55, 839. B)Us e10% becauset hel umps um paymentof$62, 741i sgrea t ert hant he10% di s count edval ueof $ 55 , 8 3 9. C)Us e8% becauset hel umps um paymentof$63, 017i sgreat ert hant he10% di s count edval ueof$56, 447. D)Us e10% becauset hel umps um paymentof$63, 017i sgreat ert hant he10%di s count edval ueof $ 56 , 4 4 7. Answer :C Expl anat i on:C)PV=

=

=$63, 016. 96, where as



=$ 5 6 , 4 4 7 . 3 9

1 7 )Yourp ar t ss uppl i e rg i v e sy ouo ne qua r t e ro faye a rt opa yf orp a r t so r de r e dt o da y , o ro ffe r sy o ua di s c o unti fy oupa yc a s ha tpur c h a s e . Yo uha v ej us tpur c h a s e d$ 7 3 , 5 0 0wo r t ho fpa r t sf r o my ours uppl i e r andt hedi s counti satanannualr at eof8%.How muchwi l lyoupayf ort hepar t si fyoupayt oday? A)$ 7 3 , 5 0 0 B)$ 72 , 0 99 C)$ 6 8, 0 5 6 D)$ 7 2 , 0 4 6 Answer :B Expl anat i on:B)PV=

=

MODE=END I NPUT . 25 8 KEY N I /Y CPT 7 2, 09 9. 36

=$ 7 2 , 0 9 9 . 3 6

? PV

0 PMT

73, 500 FV


1 8)ThePr e s e ntVa l ueI nt e r e s tF ac t or( PVI F)i st her e c i pr oc a loft heFut ur eVa l ueI n t e r e s tF ac t or( FVI F) . Ans we r :TRUE Di ff:1 T opi c :3 . 2Pr e s e ntVa l uea ndDi s c o unt i ng AACS B:3An a l y t i c a lThi n ki n g LO:3 . 2Ca l c u l a t ep r e s e n tv a l ue sa ndunde r s t a nddi s c o unt i ng .

1 9 )Whe ns o l vi ngf o rapr e s e n tv al ue ,t hei nt e r e s tr a t ei sc o mmo nl yr e f e r r e dt oast hec o mpo undr a t e ,b ut whe ns o l vi ngf ort hef ut ur ev al ue ,t hei nt e r e s tr a t ei sc a l l e dt hedi s c o untr a t e . Ans we r :F ALSE Ex pl a na t i o n:Whe ns o l vi ngf o raF UTUREv a l uet hei nt e r e s tr a t ei sc o mmo nl yr e f e r r e dt oa st he c o mpo undr a t eb utwhe ns o l vi ngf o rt hePRES ENTv a l uet hei nt e r e s tr a t ei sc a l l e dt hedi s c o untr a t e . Di ff:1 T opi c :3 . 2Pr e s e ntVa l uea ndDi s c o unt i ng AACS B:3An a l y t i c a lThi n ki n g LO:3 . 2Ca l c u l a t ep r e s e n tv a l ue sa ndunde r s t a nddi s c o unt i ng .

2 0)Gi v ena ni nt e r e s tr a t eof0 %,t hepr e s e ntv al ueof$ 1 , 5 0 0t ober e c e i v ed5ye a r si nt hef ut ur ei sl e s st ha n $ 1, 5 00 . Ans we r :F ALSE Expl anat i on:PV=

=

=$1, 500.



2 1 )Co ns i de rt heTVM e qua t i on:Pr e s e n tv a l ue sa ndi nt e r e s tr a t e sa r ei n ve r s e l yr e l a t e d. Ans we r :TRUE Di ff:1 T opi c :3 . 2Pr e s e ntVa l uea ndDi s c o unt i ng AACS B:3An a l y t i c a lThi n ki n g LO:3 . 2Ca l c u l a t ep r e s e n tv a l ue sa ndunde r s t a nddi s c o unt i ng .

2 2 )Co ns i de rt heTVM e qua t i on:Thegr e a t e rt hei nt e r e s tr a t e ,o t h e rt hi ngsr e ma i ni nge qua l ,t hegr e a t e r t hepr e s e ntv al ue . Ans we r :F ALSE Ex pl a na t i o n:TheS MALLERt hei nt e r e s tr a t e ,o t he rt hi ngsr e ma i ni nge qua l ,t heg r e a t e rt hepr e s e n tv al ue . Di ff:1 T opi c :3 . 2Pr e s e ntVa l uea ndDi s c o unt i ng AACS B:3An a l y t i c a lThi n ki n g LO:3 . 2Ca l c u l a t ep r e s e n tv a l ue sa ndunde r s t a nddi s c o unt i ng .

23)Amyhasal wayspl annedt osa veenoughmoneyt opaycas hf orherfir s tnew car .I fAmyi ncr eas est he r a t es hee a r nso nhe rs a vi ng s ,t he ns h ewi l lha v et os a v emo r emo ne yt o da yt obuyhe rc a ra tt hes a me da t ei nt hef ut ur e . Ans we r :F ALSE Ex pl a na t i o n:I fAmyi nc r e a s e st her a t es hee a r nso nhe rs a vi ng s ,t he ns h ec a ns a v eLES Smo ne yt o da yt o buyhe rc a ri nt hef ut ur e . Di ff:1 T opi c :3 . 2Pr e s e ntVa l uea ndDi s c o unt i ng AACS B:3An a l y t i c a lThi n ki n g LO:3 . 2Ca l c u l a t ep r e s e n tv a l ue sa ndunde r s t a nddi s c o unt i ng .

2 4 )$ 1 , 0 0 0r e c e i v e d5y e a r sf r o mt o da ydi s c o unt e da ta na nnua lr a t eof1 0 % ha sas ma l l e rp r e s e ntv a l ue t ha n$ 1 , 0 0 0r e c e i v e d1 0ye a r sf r o mt o da ydi s c o unt e da ta na nnua lr a t eo f5 %. Ans we r :F ALSE Expl anat i on:PV=

=

=$ 6 20 . 9 2a nd

=$ 6 1 3 . 9 1


2 5 )Co ns i de rt heTVM e q ua t i o n:Pr e s e ntv a l uea ndt i mepe r i o da r ei n ve r s e l yr e l a t e d. Ans we r :TRUE Di ff:1 T opi c :3 . 2Pr e s e ntVa l uea ndDi s c o unt i ng AACS B:3An a l y t i c a lThi n ki n g LO:3 . 2Ca l c u l a t ep r e s e n tv a l ue sa ndunde r s t a nddi s c o unt i ng .


2 6 )Wr i t et hee qua t i o nf orpr e s e n tv a l ue .Ho wa r epr i c e sa ndi nt e r e s tr a t e sr e l a t e d?Re f e rt oy oure q ua t i o n whe na ns we r i ngt h efir s tpa r toft hi sq ue s t i o n.Gi v ea ne x a mpl eo far e a l wo r l ds i t ua t i o ni nwhi c h kno wi ngt h er e l a t i ons h i pb et we e npr i c e sa ndi nt e r e s tr a t e swoul db eva l ua bl e . Ans we r :F r o mt hepr e s e ntv a l uee q ua t i o n,PV=F V×

,t hes t ude nts h oul dunde r s t a ndt ha tpr i c e s

( i . e . ,pr e s e ntva l ue s )a r ei nve r s e l yr e l a t e dt oi nt e r e s tr a t e s .Ani nc r e a s ei nonel e adst oade c r e a s ei nt he o t he ri fweho l dt heo t he ri n put sc o ns t a nt .Wes e et hi si nma n ypl a c e si nt hee c o no mys u c ha st hene g a t i v e i mpa c tons t oc kandb ondpr i c e swhe ni nt e r e s tr a t e sr i s eo ra r ee x pe c t e dt or i s e . Di ff:2 T opi c :3 . 2Pr e s e ntVa l uea ndDi s c o unt i ng AACS B:3An a l y t i c a lThi n ki n g LO:3 . 2Ca l c u l a t ep r e s e n tv a l ue sa ndunde r s t a nddi s c o unt i ng .

2 7 )Ha r o l d' sp ar e nt sh a v eo ffe r e dhi m a$ 1 0 , 0 0 0hi g hs c ho olgr a dua t i o ng i f twi t ha no pt i o nf o ra no t he r $ 20 , 0 0 0upongr a dua t i onf r o mc o l l e gei nf oury e a r s . Hi sf r i e ndst e l lhi mt hi si sa$ 3 0, 0 00gi f tf r o m hi s pa r e nt s , b utHa r o l da l r e a dykno wss o me t hi ngab outt het i mev a l ueo fmo ne y . I ft hee x pe c t e di nfla t i o n r a t eo ve rt hene x tf o ury e ar si se x pe c t e dt obe4 % pe ry e ar ,wha tdoe sHa r o l dt hi nkt hegi f ti swo r t hi n t oda y ' sdo l l a r s ?Ho ws h oul dhee x pl a i nhi st hi nki ngt ohi sf r i e nds ? Ans we r :F i r s t ,Ha r o l dmus tc a l c ul a t et hePVofhi sg i f t s . Hec a l c ul a t e sav al uee qua lt o$1 0 , 0 0 0+ 2 7 , 0 9 6 . 0 8. =$ Ha r o l ds h oul de x pl a i nt ohi sf r i e ndst ha tado l l a rt oda yha sadi ffe r e n tv al uet ha nado l l a ri n t hef ut ur eduet oo ppo r t uni t i e sa ndpur c h a s i ngpo we r .Thepr o mi s eof$ 2 0 , 0 0 0i nf o ury e a r s , whi l e g e ne r o us , i swo r t hl e s st ha n$ 2 0 , 0 0 0t o da ybe c a u s ey oumus tf o r e g oc o ns u mpt i o nf o rape r i o do ft i me . Whenyouar eabl et ous et hemoneyi nt hef ut ur e, goodswi l lcos tmoret hant heydonow.Thus ,youwi l l beabl et oc ons umef e we rgoods .I naddi t i on,i fyouhadt hemone ynow youwoul dha vet heoppor t uni t y t oi nv es ti t , s ot ha ti nf oury e ar st heva l uec oul de x c e e d$ 20 , 0 00 . Di ff:3 T opi c :3 . 2Pr e s e ntVa l uea ndDi s c o unt i ng AACS B:3An a l y t i c a lThi n ki n g LO:3 . 2Ca l c u l a t ep r e s e n tv a l ue sa ndunde r s t a nddi s c o unt i ng .

28)Compar eandcont r as tt hedi s countr at ewi t ht hecompound( orgr owt h)r at e. Ans we r :The s er a t e sa r ea c t ua l l yt hes a mev a l uei nt heTVM e q ua t i o n,b utt he yt a k eondi ffe r e ntna me s n,t whenus edf ordi ffer entpur poses .I nt heequat i onFV=PV×( 1+r ) he" r "i sr e f e r r e dt oa st h egr o wt h r a t eorc o mpo undr a t ebe c a us ei tr e pr e s e nt st her a t ea twhi c ht hei ni t i a lPVi sg r o wi ngt ot hef ut ur eva l ue . I nt hee qua t i o nPV=F V×

,t he" r "r e pr e s e n t st hedi s c o untr a t eo rt her a t ea twhi c ht heFVi s

r e duc e dt or e pr e s e ntt hec ur r e n to rpr e s e n tv a l ue . Di ff:2 T opi c :3 . 2Pr e s e ntVa l uea ndDi s c o unt i ng AACS B:3An a l y t i c a lThi n ki n g LO:3 . 2Ca l c u l a t ep r e s e n tv a l ue sa ndunde r s t a nddi s c o unt i ng .


3.3 One Equation and Four Variables 1 /n 1)I nt heequat i onr=( FV/PV) -1 ,t heri ss ome t i me sr e f e r r e dt oast he_ __ __ _ __ . A)i nt e r e s tr a t e B)di s c o untr a t e C)growt hr at e D)Al lo ft hea bo v e Answer :D Di ff:1 T opi c :3 . 3OneE qua t i o na ndFo urVa r i a b l e s AACSB:1Wr i t t enandOr alCommuni c at i on LO:3 . 3Ca l c u l a t ei mpl i e di nt e r e s tr a t e sa n dwa i t i ngt i mef r o mt het i mev a l ueo fmo ne ye qua t i o n.

2 )Theq ue s t i o n" Ho w muc hwi l lIha v ei nmya c c o unta tas p e c i ficpo i nti nt hef ut ur e , g i v e nas p e c i fic i nt e r e s tr a t e ? "i sb e s ta ns we r e db ywhi c hf o r mo ft heTVM e q ua t i o n? A)FV= n B)FV=PV×( 1+r ) 1/nC)FV=( FV/PV) 1 D) FV= Answer :B Di ff:1 T opi c :3 . 3OneE qua t i o na ndFo urVa r i a b l e s AACSB:1Wr i t t enandOr alCommuni c at i on LO:3 . 3Ca l c u l a t ei mpl i e di nt e r e s tr a t e sa n dwa i t i ngt i mef r o mt het i mev a l ueo fmo ne ye qua t i o n.

3 )Theque s t i on" Wha ti st hec ur r e ntv al ueo fa na mountofc a s ht ha twi l lber e c e i v e da tas pe c i fict i mei n t hef ut ur e? "i sbestans wer edbywhi chf orm oft heTVM equat i on? A)PV= n B)PV=PV×( 1+r ) 1/n-1 C)PV=( FV/PV) D)PV= Answer :A Di ff:1 T opi c :3 . 3OneE qua t i o na ndFo urVa r i a b l e s AACS B:3An a l y t i c a lThi n ki n g LO:3 . 3Ca l c u l a t ei mpl i e di nt e r e s tr a t e sa n dwa i t i ngt i mef r o mt het i mev a l ueo fmo ne ye qua t i o n. Hmwr kQue s t i o ns :*T a k e nf r o m" Pr e ppi ngf o rE x a ms "q ue s t i o nsa tt h ee ndo ft h ec h ap t e r .


4)Theques t i on" Atwhatr at ei smymoneygr owi ngovert i me? "i sbes tanswer edbywhi chf orm oft he TVM e quat i on? A)r= n B)r=PV×( 1+r ) 1/n-1 C)r=( FV/PV) D)r= Answer :C Di ff:1 T opi c :3 . 3OneE qua t i o na ndFo urVa r i a b l e s AACSB:1Wr i t t enandOr alCommuni c at i on LO:3 . 3Ca l c u l a t ei mpl i e di nt e r e s tr a t e sa n dwa i t i ngt i mef r o mt het i mev a l ueo fmo ne ye qua t i o n.

5 )Theque s t i o n" Ho wl o ngwi l lIha v et owa i tt or e a c hac e r t a i nf ut ur ev al ue ? "i sb e s ta ns we r e db ywhi c h f or m oft heTVM equat i on? A)n= n B)n=PV×( 1+r ) 1 /n-1 C)n=( FV/PV) D)n= Answer :D Di ff:1 T opi c :3 . 3OneE qua t i o na ndFo urVa r i a b l e s AACSB:1Wr i t t enandOr alCommuni c at i on LO:3 . 3Ca l c u l a t ei mpl i e di nt e r e s tr a t e sa n dwa i t i ngt i mef r o mt het i mev a l ueo fmo ne ye qua t i o n.

6 )Di vi de ndgr o wt hr a t ei si mpor t a ntt oma nyi n ve s t or s . Yo ua r ec ons i de r i ngi n ve s t i ngi nafir ma f t e r l o oki nga tt hefir m' sdi v i de ndso v e ras e v e ny e a rp e r i o d.Att hee ndo ft hey e a r2 0 0 2 ,t hefir m pa i da di vi de ndo f$ 1 . 1 5 .Aty e a r e nd2 0 0 9 ,i tpa i dadi vi de ndo f$ 1 . 8 4 .Wha twa st hea v e r a g ea nnua lgr o wt hr a t e o fdi vi de ndsf ort hi sfir m? A)7 . 2 5 % B)9 . 8 6% C)6 . 9 4 % D)The r ei sn ote no ug hi nf o r ma t i o nt oa ns we rt hi sq ue s t i o n. Answer :C 1 /n 1/7 . 9 4 % Expl anat i on:C)r=( FV/PV) -1=( $ 1. 8 4 /$ 1. 1 5) -1=6 MODE=END I NPUT 7 KEY N CPT 6. 94

? I /Y

1. 15 PV

0 1. 84 PMT FV

Di ff:2 T opi c :3 . 3OneE qua t i o na ndFo urVa r i a b l e s AACS B:3An a l y t i c a lThi n ki n g LO:3 . 3Ca l c u l a t ei mpl i e di nt e r e s tr a t e sa n dwa i t i ngt i mef r o mt het i mev a l ueo fmo ne ye qua t i o n.


7 )F oury e a r sa go ,Ro be r t ' sa n nua ls a l a r ywa s$ 5 2 , 5 0 0 .T oda y , hee a r n s$ 7 3 , 8 0 0.Wha tha sb e e nt hea v e r a g e a nnua lr a t eofgr o wt ho fRo be r t ' ss a l a r y ? A)$ 5 , 3 2 5pe ry e a r B)1 0. 3 8% C)4 1 . 5 2 % D)8 . 8 9 % Answer :D 1/n 1/4 . 8 9 % Expl anat i on:D)r=( FV/PV) -1=( $ 73 , 8 00 /$ 52 , 5 00 ) -1=8 MODE=END I NPUT 4 KEY N CPT 8 . 89

? I /Y

5 2, 5 00 PV

0 73, 800 PMT FV


8 )Y ouga v ey ourl i t t l es i s t e rt wor a bbi t sf orEa s t e rt hr e ey e ar sa goa ndno ws heha s8 4oft hec ut el i t t l e bunni e s .Wha ti st hea ve r agea nnualr at eofi nc r e as ei nt henumbe rofr abbi t syours i s t e rowns ?Not e :Your pa r e nt sa r eno tv e r ypl e a s e dwi t hy our i g htno w. A)2 4 7 . 6 0 % B)1 4. 0 0% C)4 1 0. 0 0 % D)TheTVM equat i onsar edes i gnedf orc ur r encyamount sandc annotbeus edf ornonfinanc i al c a l c ul a t i onss uc ha st hi so ne . Answer :A 1 /n 1 /3 47 . 6 0% Expl anat i on:A)r=( FV/PV) -1=( 8 4 /2 ) -1=2 MODE=END I NPUT 3 ? KEY N I /Y CPT 24 7. 60

2 PV

0 84 PMT FV



9 )S i mps o nCons t r u c t i onha ds a l e ss e v e ny e a r sa goo f$ 2 , 1 5 0 , 0 0 0 .Thi sy e a rt he i rs a l e shi t$ 4 , 6 0 0 , 0 0 0.Wha t ha sb e e nS i mps o n' sa v e r a g eannua lr a t eofgr o wt ho fs a l e s ? A)3 0 . 5 6 % B)1 1. 4 8% C)$ 3 5 0 , 0 0 0pe ry e a r D)Noneoft heabove Answer :B 1/n-1=( 1 /7 1 . 4 8 % Expl anat i on:B)r=( FV/PV) $ 4, 6 00 , 0 00 /$ 2 , 1 5 0, 0 0 0) -1=1 MODE=END I NPUT 7 KEY N CPT 11. 48

? I /Y

2 , 15 0, 00 0 0 PV PMT

4, 600, 000 FV


1 0)TheMi l l vi l l eSc hoolDi s t r i c tha d3 , 0 71s t ude nt se nr o l l e dfiveye a r sa go.T oda y , t hedi s t r i c te nr o l l me nt i s2 , 4 1 8s t ude nt s . Wha tha sb e e nt hea nnua lr a t eofc h ang eo fs t ude nte nr ol l me nti nt heMi l l vi l l eS c ho ol Di s t r i c to ve rt hi st i mepe r i od? A)5 . 4 0% B)4 . 2 5% C)4 . 6 7% D)4 . 2 5 % Answer :C 1 /n 1/5 Expl anat i on:C)r=( FV/PV) -1=( 2 , 4 1 8/3 , 0 71 ) -1=4 . 6 7 % MODE=END I NPUT 5 KEY N CPT 4. 67

? 3 , 071 I /Y PV

0 PMT

2, 418 FV

Di ff:2 T opi c :3 . 3OneE qua t i o na ndFo urVa r i a b l e s AACS B:3An a l y t i c a lThi n ki n g LO:3 . 3Ca l c u l a t ei mpl i e di nt e r e s tr a t e sa n dwa i t i ngt i mef r o mt het i mev a l ueo fmo ne ye qua t i o n. Hmwr kQue s t i o ns :*T a k e nf r o m" Pr e ppi ngf o rE x a ms "q ue s t i o nsa tt h ee ndo ft h ec h ap t e r .


1 1 )Y ouc ur r e n t l yha v e$2 , 5 0 0i n ve s t e da ta na nnua lr a t eof8 %.Ho wl ongwi l li tt a kef ort hi si n ve s t me ntt o gr o wt oav al ueo f$ 3 , 5 0 0 ? A)4 . 3 7ye a r s B)5 . 0 0y e ar s C)5 . 6 0y e a r s D)8 . 0 3ye a r s Answer :A Expl anat i on:A)n= MODE=END I NPUT ? KEY N CPT 4 . 37

= 8 I /Y

=4 . 3 7y ea r s

2, 500 PV

0 PMT

3 , 500 FV


1 2 )Y ouha v es a v e d$ 1 , 2 0 0f o raus e dmo t o r c y c l et ha tha sac ur r e n tpr i c eof$ 1 , 5 0 0 .I fy ourmo ne yi ss i t t i ng i na na c c o unte a r n i ng2 . 5 0 % pe ry e a r ,ho wl o ngwi l li tt a kef o rt hi sa c c ountt ogr o wt o$1 , 5 0 0 ?No t e :The mo t o r c y c l e ' sp r i c ema yha v ec h ang e db yt het i mey oura c c o untr e a c h e sav a l ueo f$ 1 , 5 0 0 . A)9. 04mont hs B)9 . 0 4y e ar s C)4 . 2 5y e a r s D)4. 25mont hs Answer :B Expl anat i on:B)n= MODE=END I NPUT ? KEY N CPT 9. 0 4

= 2. 5 I /Y

=9 . 0 4y ea r s

1, 20 0 PV

0 PMT

1 , 500 FV



13)Madi s oni st aki ngoverasChi efMar ket i ngOffice ratMi dWes tGr aphi cs .Shehaspl edgedt oi ncr eas e s a l e sf r o mt he i rc ur r e ntl e v elo f$ 1 2, 0 00 , 0 00atar a t eof1 0% pe ry e arunt i lt hefir m hi t ss a l e sof$ 2 0, 0 00 , 0 00 pe ry e a r . Ho wl ongwi l li tt a keMa di s o nt ohi tt het a r g e tg oa la tt hi sr a t eofi nc r e a s e ? A)7 . 6 7ye a r s B)1 . 5 3y e ar s C)5 . 3 6y e a r s D)Att ha tr a t e ,Ma di s o nwi l lne ve rr e a c ht het a r g e ts a l e sl e v eli nhe rl i f e t i me . Answer :C Expl anat i on:C)n= MODE=END I NPUT ? KEY N CPT 5. 36

. 3 6y ea r s =5

= 10 I /Y

1 2, 00 0, 00 0 PV

0 PMT

2 0, 00 0, 0 00 FV


1 4 )Upo nt a ki nghi sfi r s tj o bo utofc o l l e g e ,y ourDa de a r n e da na nnua ls a l a r yof$ 3 8, 0 0 0ands e tagoa lt o e a r n$ 1 00 , 0 0 0pe ry e a r .I fhi ss a l a r yi nc r e a s e da ta na v e r a g eannua lr a t eof1 2 %,ho wl o ngdi di tt a ket o r e a c hhi sg oa l ? A)Att ha tr a t eofgr o wt h,y ourDa ds t i l lha sno te a r ne d$ 1 0 0, 0 0 0i nas i ngl ey e ar . B)2 . 6 3y e ar s C)2 6 . 3 1ye a r s D)8 . 5 4ye a r s Answer :D Expl anat i on:D)n= MODE=END I NPUT ? KEY N CPT 8. 54

= 12 I /Y

=8 . 5 4y ea r s

38, 0 00 PV

0 PMT

100, 000 FV



1 5 )Y ourg r a n df a t he rl i ke st ot e l lt hes t or ya bo utho w hes t a r t e dwi t h5 0he a do fc a t t l eonhi sr a nc ha nd gr e wt her a nc ht o1 , 0 0 0he a do fc a t t l e . Hes a i d" Mypl a nwa ss i mpl e :gr o wt henumb e ro fhe a do fc a t t l ea t ar a t eo f1 0 % pe ry e a r . "Yourgr a ndf a t he rr e a c he dhi sg oa lb ef o r eher e t i r e d.Ho wl ongdi di tt a kehi m? A)1 8 . 6 3ye a r s B)3 1. 4 3ye a r s C)2 5 . 2 2ye a r s D)4 7 . 6 5ye a r s Answer :B Expl anat i on:B)n= MODE=END I NPUT ? KEY N CPT 31 . 43

1. 4 3ye a r s =3

= 10 I /Y

5 0 PV

0 PMT

1 , 000 FV


1 6 )Co ns i de rt heTVM e q ua t i o n:t hev a r i a bl e" r "ma ybede fine da st hedi s c o untr a t eo rt heg r o wt hr a t e dependi nguponhow t heequat i oni sbei ngus ed. Ans we r :TRUE Di ff:1 T opi c :3 . 3OneE qua t i o na ndFo urVa r i a b l e s AACSB:1Wr i t t enandOr alCommuni c at i on LO:3 . 3Ca l c u l a t ei mpl i e di nt e r e s tr a t e sa n dwa i t i ngt i mef r o mt het i mev a l ueo fmo ne ye qua t i o n.

1 7)Ev eni fy oua r egi v enapr e s e ntv al ue ,af ut ur ev a l ue ,a nda ni nt e r e s tr a t e ,s o l vi ngf ort het i mepe r i od " n"i ss t i l lat r i al ande r r orpr oc es s . Ans we r :F ALSE Ex pl a na t i o n:n= Di ff:1 T opi c :3 . 3OneE qua t i o na ndFo urVa r i a b l e s AACS B:3An a l y t i c a lThi n ki n g LO:3 . 3Ca l c u l a t ei mpl i e di nt e r e s tr a t e sa n dwa i t i ngt i mef r o mt het i mev a l ueo fmo ne ye qua t i o n.

1 8)Ev eni fy oua r eg i v enapr e s e ntv al ue ,as i ngl ef ut ur ev a l ue ,a ndat i mepe r i od,s o l vi ngf ort her a t eof r e t ur n,r ,i ss t i l lat r i al a nde r r orpr oc es s . Ans we r :F ALSE 1/n-1 Expl anat i on:r=( FV/PV) Di ff:1 T opi c :3 . 3OneE qua t i o na ndFo urVa r i a b l e s AACS B:3An a l y t i c a lThi n ki n g LO:3 . 3Ca l c u l a t ei mpl i e di nt e r e s tr a t e sa n dwa i t i ngt i mef r o mt het i mev a l ueo fmo ne ye qua t i o n.


1 9 )Ot he rt hi ngsr e ma i ni nge qua l ,t hepr i c et o da ya ndt hegr o wt hr a t ea r ei n ve r s e l yr e l a t e d. Ans we r :TRUE 1/n-1 Expl anat i on:r=( FV/PV) Di ff:1 T opi c :3 . 3OneE qua t i o na ndFo urVa r i a b l e s AACS B:3An a l y t i c a lThi n ki n g LO:3 . 3Ca l c u l a t ei mpl i e di nt e r e s tr a t e sa n dwa i t i ngt i mef r o mt het i mev a l ueo fmo ne ye qua t i o n.

2 0)Youha v ej us twont heuni v er s i t yl o t t e r y . I fy ougr a dua t e ,y ouwi l lr e c e i v ear e f unde qua lt ot h e amountoft ui t i onyoupai di nyourfir s tf ouryear sofs c hool .However ,youneedmoneynow andafir m t ha ts p ec i a l i z e si nbuyi nge x pe c t e df ut ur ec a s hflo wsh aso ffe r e dt odi s c o untt hel o t t e r ywi nni ngsa tar a t e o f8 %a ndpa yy ouc a s ht o da yi ne x c h a ng ef o ry o urf ut ur el o t t e r ywi nni ng s .S i nc ey o uha v es t udi e d fina nc e , y oui ns i s tt ha tt he ydi s c o untt hec a s hflo wsa t1 2 %i ns t e a do f8 %b e c a us et he r ei ss o mer i s ka st o t hec e r t a i nt yo fy ourgr a dua t i ng.I ft hefir ma gr e e st oyo urde ma nd,t he nt hi sme a nst he ywi l li nc r e a s et he pr e s e ntv a l ueofwha tt he ywi l lpa yyo ut o da y . Ans we r :F ALSE Ex pl a na t i o n:Ani nc r e a s ei nt hedi s c o untr a t ewi l lde c r e a s et hepr e s e n tv al ueo fwha tt hefir m wi l lpa y yout oday . Di ff:2 T opi c :3 . 3OneE qua t i o na ndFo urVa r i a b l e s AACS B:3An a l y t i c a lThi n ki n g LO:3 . 3Ca l c u l a t ei mpl i e di nt e r e s tr a t e sa n dwa i t i ngt i mef r o mt het i mev a l ueo fmo ne ye qua t i o n.

2 1 )Cur r e nta nnua ldi vi de ndsf o rS i mps o nsF r oz e nF oo dsI nc . ,a r e$ 1 . 3 5pe rs h ar e .F oury e ar sa g o, di vi de ndspe rs h a r ewe r ee x a c t l y$ 1 . 0 0 .Wha tha sb e e nt her a t eo fg r o wt hf o rS i mps o ns ' di vi de ndsp e r s h a r e ? 1/n 1/4 Ans wer :r=( FV/PV) -1=( $ 1. 3 5/$ 1 . 0 0 ) -1=7 . 7 9 % pe ry e a r . Di ff:2 T opi c :3 . 3OneE qua t i o na ndFo urVa r i a b l e s AACS B:3An a l y t i c a lThi n ki n g LO:3 . 3Ca l c u l a t ei mpl i e di nt e r e s tr a t e sa n dwa i t i ngt i mef r o mt het i mev a l ueo fmo ne ye qua t i o n.

2 2 )Aty ourb i r t h,y ourgr a ndpa r e nt sp ut$ 5 , 0 0 0i nt oac o l l e g ef undf o ry o u.No wy ouwa ntt ous et hef und t opa yyo urfi r s ty e a ro fc o l l e g ec o s t so f$ 2 3 , 0 0 0 .T oha v ee no ug hmo ne yi ny ourc o l l e g ef undf o ry our s t at edpur pose, whatannualr at eofr et ur nwoul dhavet ohavebeenear nedont heacc ountoveran18y e a rpe r i o d? 1/n 1/18 Ans wer :r=( FV/PV) -1=( $ 23 , 0 00 /$ 5, 0 00 ) -1=8 . 8 5 % pe ry e a r . Di ff:2 T opi c :3 . 3OneE qua t i o na ndFo urVa r i a b l e s AACS B:3An a l y t i c a lThi n ki n g LO:3 . 3Ca l c u l a t ei mpl i e di nt e r e s tr a t e sa n dwa i t i ngt i mef r o mt het i mev a l ueo fmo ne ye qua t i o n.


2 3 )Y ouma dey ourfi r s t$ 3 , 0 0 0de po s i tt o da yi nt oar e t i r e me nta c c o unte a r n i nga na v e r a g ea nnua lr a t eof 6 %. Ho wl o ngwi l li tt a key ourde pos i tt or e a c hava l ueo f$ 5 0, 0 0 0?Ho wl o ngwi l li tt a kei fi ns t e a dy ou i n ve s tt hemo ne yi nt oa na c c o unte a r ni ng1 0% pe ry e a r ?Af t e rma ki ngyo urc a l c u l a t i o ns , ho w do e st hi s i nf o r ma t i o na ffe c ty ourde c i s i o nma ki ngr e g a r d i ngl o ng t e r mi n ve s t me nt s ? Ans we r :n=

=

=4 8 . 2 8y e a r sv s .

=2 9 . 5 2y e a r s .

Hope f ul l y ,t hes t ude ntwi l lr e c ogni z et ha tl o wi nt e r e s tr a t e s , whi l eof t e na s s o c i a t e dwi t hl o we r r i s k i n ve s t me nt s , ha v et her i s koft a ki ngt o ol ongt ome e tf ut ur eva l ueob j e c t i v e s .Wi t ht i mef r a me ss u c ha si n t hi spr o bl e m,i nv es t or sa r eof t e nwi l l i ngt oi nv es ti nhi ghe rr i s k-hi ghe re x pe c t e dr e t ur ni nv es t me nt s . Di ff:3 T opi c :3 . 3OneE qua t i o na ndFo urVa r i a b l e s AACS B:3An a l y t i c a lThi n ki n g LO:3 . 3Ca l c u l a t ei mpl i e di nt e r e s tr a t e sa n dwa i t i ngt i mef r o mt het i mev a l ueo fmo ne ye qua t i o n.

3.4 pplications o! t"e #ime Value o! $one% Equation 1 )I n1 9 3 0 ,t hehi ghe s tpa i dpl a y e ri nma j o rl e a g ueb a s e b a l lwa sB ab eRut ho ft heNe w Yo r kYa nk e e s , wi t h a na nnua ls a l a r yof$ 8 0 , 0 0 0 .I n2 0 05 ,t hehi ghe s tpa i dpl a y e ri nma j o rl e a gueb as e b a l lwa sAl e xRodr i gue z , a l s oo ft heNe w Yo r kYa nk e e s , wi t has a l a r yo f$ 2 5 , 0 0 0 , 0 0 0 .Wha twa st hea v e r a g ea nnua lr a t eo fgr o wt hi n t het opba s e ba l ls a l a r yo ve rt hi st i mepe r i od? A)7 . 9 6 % B)1 8. 7 0% C)3 . 3 1 % D)4 . 1 7 % Answer :A 1 /n 1/75=7 Expl anat i on:A)r=( FV/PV) -1=( $ 2 5, 0 0 0, 0 0 0/$ 80 , 0 00 ) . 9 6 % MODE=END I NPUT 75 KEY N CPT 7. 96

? I /Y

8 0, 00 0 PV

0 2 5, 00 0, 0 00 PMT FV

Di ff:2 T opi c :3 . 4Appl i c a t i o nso ft heT i meVa l ueo fMo ne yEq ua t i o n AACS B:3An a l y t i c a lThi n ki n g LO:3 . 4Appl yt het i mev a l ueo fmo ne ye qua t i o nus i ngf o r mul a ,c a l c ul a t o r ,a nds p r e a ds h e e t .


2 )I n1 9 7 0,b ef or et hee r aofma j o rl e a gueba s e b a l lf r e ea ge nc y , t hemi ni mum pl a y e rs a l a r ywa s$ 1 2 , 0 0 0. I n 1975, t hemi ni mum s al ar ywas$ 16, 000. Whatwast heaver ageannualgrowt hi nt hemi ni mum s al ar yi n ma j o rl e a gueb as e b a l lo ve rt hos efiv eye a r s ? A)1 3 . 4 0 % B)2 . 6 7% C)5 . 9 2 % D)1 5 . 0 0 % Answer :C 1 /n 1 /5 Expl anat i on:C)r=( FV/PV) -1=( $ 16 , 0 00 /$ 12 , 0 00 ) -1=5 . 9 2 % MODE=END I NPUT 5 KEY N CPT 5. 92

? I /Y

12, 000 PV

0 PMT

16, 0 00 FV


3 )I n1 9 7 5,t hee r ao fma j orl e a gueba s e b a l lf r e ea g e nc ybe g an.Thea ve r a gepl a y e rs a l a r ywa s$ 1 6, 0 0 0. I n 1980, t heaver agesal ar ywas$30, 000. Whatwast heaver ageannualgrowt hi nt hemi ni mum s al ar yi n ma j o rl e a gueb as e b a l lo ve rt hos efiv eye a r s ? A)3 7 . 5 0 % B)1 3. 4 0% C)5 . 9 2 % D)1 0 . 6 7 % Answer :B 1 /n 1/5=1 3. 4 0% Expl anat i on:B)r=( FV/PV) -1=( $ 30 , 0 00 /$ 16 , 0 00 ) MODE=END I NPUT 5 KEY N CPT 13 . 40

? I /Y

16, 000 0 PV PMT

30, 000 FV



4 )Av e r a g eU. S .wa g e si n1 9 9 0we r e$ 2 8 , 9 6 0 ,f a rl a r g e rt ha nt hea v e r a g ewa g ei n1 9 3 0of$ 1 , 9 7 0 .Wha twa s t hea v e r a g eannua li nc r e a s ei nwa ge so v e rt hi s6 0 y e a rpe r i o d? A)3 . 3 1 % B)2 . 4 5% C)2 4 . 5 0 % D)4 . 5 8 % Answer :D 1/n 1/60=4 . 5 8 % Expl anat i on:D)r=( FV/PV) -1=( $ 28 , 9 60 /$ 1, 9 70 ) MODE=END I NPUT 60 KEY N CPT 4. 58

? I /Y

1, 970 PV

0 PMT

28, 960 FV

Di ff:2 T opi c :3 . 4Appl i c a t i o nso ft heT i meVa l ueo fMo ne yEq ua t i o n AACS B:3An a l y t i c a lThi n ki n g LO:3 . 4Appl yt het i mev a l ueo fmo ne ye qua t i o nus i ngf o r mul a ,c a l c ul a t o r ,a nds p r e a ds h e e t . Hmwr kQue s t i o ns :*T a k e nf r o m" Pr e ppi ngf o rE x a ms "q ue s t i o nsa tt h ee ndo ft h ec h ap t e r .

5 )Ga s ol i nec o s t$ . 1 0pe rg a l l oni n1 93 0 .Ov ert hene x t6 0y e ar s ,t hepr i c er os ea ta na v er a ger a t eof4 . 4 2% pe ry e a r .Ba s e do nt hi si nf o r ma t i on,wha twa st hea v e r a g epr i c eo faga l l ono fg a si n1 9 9 0? A)$ 1. 3 4pe rg a l l on B)$ 1. 5 3pe rg al l on C)$ 2. 6 5pe rg a l l on D)$ 2. 7 5pe rg a l l on Answer :A n 60=$ 1 . 3 4 Expl anat i on:A)FV=PV∗ ( 1+r ) =$ 0 . 1 0∗ ( 1 . 0 44 2) MODE=END I NPUT 60 KEY N CPT 1. 34

4. 42 I /Y

. 10 PV

0 ? PMT FV



6 )F ormuc hoft he2 0 t hc e n t ur y ,ne wc a rpr i c e sr o s ea ta na nnua lr a t eo f5 . 7 3 %.Gi v e nabe g i nni ngne wc a r pr i c eo f$ 6 0 0 ,ho wl ongdi di tt a kef ort hea ve r a gene wc a rp r i c et or i s et o$ 1 6 , 9 5 0 ?Pl e a s er o undt ot he ne ar e s ty ea r . A)40year s B)6 0ye a r s C)7 0y e a r s D)100year s Answer :B Expl anat i on:B)n= MODE=END I NPUT ? KEY N CPT 59. 96

9. 9 6ye ar s =5

= 5. 73 I /Y

6 00 PV

0 PMT

1 6, 95 0 FV

Di ff:2 T opi c :3 . 4Appl i c a t i o nso ft heT i meVa l ueo fMo ne yEq ua t i o n AACS B:3An a l y t i c a lThi n ki n g LO:3 . 4Appl yt het i mev a l ueo fmo ne ye qua t i o nus i ngf o r mul a ,c a l c ul a t o r ,a nds p r e a ds h e e t . Hmwr kQue s t i o ns :*T a k e nf r o m" Pr e ppi ngf o rE x a ms "q ue s t i o nsa tt h ee ndo ft h ec h ap t e r .

7)Buyi ngyourownhomei sof t enment i onedas" t hebesti nvest mentyoucanmake. "I n1930,t heaver age ho mes a l epr i c ewa s$ 3 , 8 4 5 .By1 9 9 0 ,t hea v e r a g eho mes a l epr i c eh a dr i s e nt o$ 1 2 3 , 0 0 0 .Wha twa st he a v e r a g ea nnua lr a t eofc h ang ei nt hepr i c eo fhous e so ve rt hi st i mepe r i o d? A)3. 42% peryear B)5. 95% peryear C)10. 12% peryear D)12. 36% peryear Answer :B 1 /n 1/60 95% peryear Expl anat i on:B)r=( FV/PV) -1=( $ 12 3 , 0 00 /$ 3, 8 45 ) -1=5. MODE=END I NPUT 60 KEY N CPT 5. 95

? I /Y

3, 845 0 123, 000 PV PMT FV



8 )Ki r b yPuc k e t tb e c a met hefir s t$ 3 , 0 0 0 , 0 0 0ma ni nma j o rl e a g ueb as e b a l li n1 9 9 0 .By20 0 8 ,ARo dwa s br i ngi ngi n$27, 500, 000pe rye a r .Di dt heannualc hangei nt hehi ghe s tannualbas e bal ls al ar yr i s emor e r a pi dl yo v e rt hi st i mepe r i o dt ha nf r o m1 9 3 0t o1 99 0 ?Ba beRut hha dt hehi g he s ts a l a r ya ndma de$ 8 0 , 0 0 0 i n1 9 30 . A)Ye s ,b e c a us et hea n nua lr a t eo fc h a ng ewa s2 9 . 1 7 %i nt hemo r er e c e n tpe r i o da ndo nl y3 6. 6 7 %i nt he e ar l i e rpe r i od. B)No ,b e c a us et hea nnua lr a t eo fc h a ng ewa s2 9 . 1 7 %i nt hemo r er e c e n tpe r i o da nd3 6 . 6 7 %i nt hee a r l i e r pe r i o d. C)Ye s , b e c a us et hea nnua lr a t eo fc h a ng ewa s1 3 . 1 0 %i nt hemo r er e c e n tpe r i o da ndo nl y6 . 2 3 %i nt he e ar l i e rpe r i od. D)The r ei sn o te no ug hi nf o r ma t i o npr o vi de dt oa ns we rt hi sq ue s t i o n. Answer :C 1 /n 1/18 Expl anat i on:C)r=( FV/PV) -1=( $ 27 , 5 00 , 0 00 /$ 3, 0 00 , 0 00 ) -1=1 3 . 1 0 % and 1/60 . 2 3 % ( $ 3, 0 00 , 0 00 /$ 8 0, 0 0 0) -1=6 Di ff:3 T opi c :3 . 4Appl i c a t i o nso ft heT i meVa l ueo fMo ne yEq ua t i o n AACS B:3An a l y t i c a lThi n ki n g LO:3 . 4Appl yt het i mev a l ueo fmo ne ye qua t i o nus i ngf o r mul a ,c a l c ul a t o r ,a nds p r e a ds h e e t .

9 )I nJ a nua r yof1 9 97 ,t heU. S .Cons u me rP r i c eI nde x( CPI )s t o oda t1 5 9 . 1 .ByJ a nua r yof2 0 11 ,t hel e v e l ha dr i s e nt o2 2 0 . 2 .Wha twa st hea v e r a g eannua lr a t eofi nfla t i o no v e rt hi st i mepe r i o da sme a s u r e db yt he CPI ? A)2 . 3 5 % B)3 . 3 1% C)2 . 9 7 % D)2 . 6 0 % Answer :A 1 /n 1/14 Expl anat i on:A)r=( FV/PV) -1=( 2 2 0. 2 /1 59 . 1 ) -1=2 . 3 5 % MODE=END I NPUT 1 4 KEY N CPT 2 . 35

? I /Y

159. 1 0 220. 2 PV PMT FV



10)Thes ur veyr es ul t sf r om t heNat i onalAs s oci at i onofCol l egesandEmpl oyer s( NACE)s how t he a v e r a g ea nnua li nc r e a s e si ns a l a r i e sf o rne wa c c o unt i nggr a dua t e st obe3 . 4 2 %s i nc et hey e a r2 0 00 .I fne w s t a r t i ngs a l a r i e si na c c o unt i ngwe r e$ 36 , 9 1 9i n2 0 0 0,wha twe r et he yi n2 0 1 1? A)$ 4 5 , 7 5 7 B)$ 46 , 7 18 C)$ 5 3, 4 4 4 D)$ 4 2 , 6 1 7 Answer :C n 11=$ Expl anat i on:C)FV=PV∗ ( 1+r ) =$ 3 6 , 9 1 9∗ ( 1 . 0 34 2) 5 3 , 4 4 4 . 1 0 MODE=END I NPUT 1 1 3. 4 2 KEY N I /Y CPT 5 3, 44 4. 10

3 6, 91 9 PV

0 ? PMT FV


1 1 )Yourfi na nc epr o f e s s ors ugg e s t st ha ty ous h oul dha v e$2 , 5 0 0 , 0 0 0i ny ourr e t i r e me ntpo r t f o l i ob e f or e y oue v e nTHI NKa b outr e t i r i ng .Re c e n t l y , y ouru nc l es o l dv a l ua b l eCa l i f o r n i ar e a le s t a t ea ndha nde dy ou ac he c kf or$ 3 00 , 0 0 0.( Thi si st hea mo unty ouha v ea f t e rpa y i ngt a x e s . Hei sn ow y ourf a v or i t eunc l e . )Ho w muc hoft he$ 3 0 0 , 0 0 0mus ty ous e ta s i det o da yi fy oui n ve s tapo r t i o no ft hemo ne ya ta na nnua lr a t eo f 8. 0% andyouwi s ht or et i r ei n35year swi t ht heamounts ugges t edbyyourfinancepr of es s or? A)$ 1 6 9 , 0 8 6 B)$ 14 , 5 08 C)$ 1 30 , 9 1 4 D)Ata na nnua lr a t eofr e t ur no f8 . 0 %,$ 3 0 0 , 0 0 0i sn otal a r g ee no ug hi n ve s t me ntt or e a c ht hego ala mo unt of$ 2, 5 00 , 0 00i n3 5y e ar s . Answer :A Expl anat i on:A)PV= MODE=END I NPUT 35 8 KEY N I /Y CPT 16 9, 08 6. 3 6

16 9, 0 86 . 3 6 =$

=

? PV

0 PMT

2, 500, 000 FV



12)Youpl ant opl acea$40, 000downpaymentonal akecabi ni nNort her nMi nnesot ai nfiveyears . I fyou i nvesti nal ongt er m CDear ni nganannualr at eof5. 50%,how muchwoul dyouneedt oi nvestt odayt o haveenoughf ort hedownpaymenti nfiveye ar s ? A)$ 3 3 , 3 2 6 B)$ 30 , 6 05 C)$ 2 4, 3 7 9 D)$ 1 8 , 2 6 4 Answer :B Expl anat i on:B)PV= MODE=END I NPUT 5 5. 5 KEY N I /Y CPT 30, 6 05. 3 7

=

=$ 3 0 , 6 0 5 . 3 7

? PV

0 PMT

4 0, 00 0 FV


1 3 )Ha r r yde c i de dhewa st i r e do fb e i ngapo orc ol l e g es t ude ntwhe nhevi s i t e dal oc a le l e c t r oni c ss t or e a nde x pe r i e nc e di t sfi ne s tho met he a t r es y s t e m.Hede t e r mi ne dt ha thewo ul di n ve s tt o da yapo r t i o no f t her e ma i ni ngmo ne yhee a r n e dl a s ts u mme rc l e a ni nga ni ma lc a g e sa tt hev e t e r i na r yc l i ni c . Hepl a nst o i n ve s tt hemo ne yi nt oa ni nt e r n a t i ona lmut ua lf undf o r3 . 5y e a r sa nde x pe c t st oe a r nana ve r a gea nnua l r a t eo fr e t ur no f1 5 %.I fHa r r ywa nt st oha v e$ 4 , 0 0 0i nt hea c c o unta tt hee ndo ft hi st i me , ho w muc hmus t hei n ve s tt o da y ? A)$ 1 , 2 5 3 B)$ 2, 0 48 C)$ 2 , 4 5 3 D)$ 2 , 5 9 1 Answer :C Expl anat i on:C)PV= MODE=END I NPUT 3. 5 15 KEY N I /Y CPT 2, 45 2. 55

2 , 4 5 2 . 5 5 =$

=

? PV

0 PMT

4, 000 FV



14)Youneed$32, 000att heendof6year s .I fyouca near n0. 625% permont h,how muchwoul dyouneed t oi nv es tt o da yt ome e ty ouro bj e c t i v e? A)$ 1 7 , 6 0 0 B)$ 18 , 3 19 C)$ 2 0, 7 3 5 D)$ 2 0 , 4 3 3 Answer :D Expl anat i on:D)PV=

2 0 , 4 3 2 . 7 0 =$

=

MODE=END I NPUT 72 . 62 5 KEY N I /Y CPT 20, 4 32. 7 0

? PV

0 MT

3 2, 00 0 FV


1 5 )Y ourf r i e ndJ o hns t a r t e dc o l l e g ea tt hea geof1 8wi t h$ 6 3, 4 5 0a l r e a dys a v e d,be c a us e1 8ye a r sa go whe nhewa sb o r nhi sp a r e n t spl a c e dmo ne yi nt oas pe c i a lc o l l e g es a v i ng sa c c o unte a r ni ng7 . 2 5 % pe ry e a r . How muchmoneydi dJ ohn' spar ent spl acei nt ohi scol l egeacc ount ? A)$ 1 8 , 0 0 0 B)$ 3, 5 25 C)$ 1 7, 2 6 2 D)$ 5 , 8 2 4 Answer :A Expl anat i on:A)PV= MODE=END I NPUT 18 7 . 25 KEY N I /Y CPT 18, 000. 32

1 8 , 0 0 0 . 3 2 =$

=

? PV

0 PMT

63, 450 FV



1 6 )Y ouk no wt ha tr e g ul a rt a x de f e r r e di n ve s t me nt sa r eapo pul a ri n ve s t me ntc h oi c ef o rma n ype o pl e pr e pa r i ngf orr e t i r e me nt .Di dy oukno wt ha ti fy oui n ve s t$ 2 , 0 0 0t oda ya nda tt hee ndo fe v e r yye a rf o r4 0 y e a r sa ta na nnua lr a t eo f1 0 %t ha ty ouwi l lha v egr o wny ourpor t f o l i ot oava l ueo f$ 9 7 5, 7 0 4att hee ndof t hatt i me?How muchoft hatf ut ur eval uedol l aramountcomesf r om t he$2, 000i nves t mentyoumade today? A)$ 9 7 5 , 7 0 4 B)$ 88 5, 1 85 C)$ 2 3, 7 9 8 D)$ 9 0 , 5 1 9 Answer :D n 40=$ 9 0 , 5 1 8 . 5 1 Expl anat i on:D)FV=PV∗ ( 1+r ) =$ 2 , 0 0 0∗ ( 1 . 10) MODE=END I NPUT 40 10 KEY N I /Y CPT 90, 518 . 51

2 , 000 PV

0 PMT

? FV


1 7 )I fy oui n ve s t$ 5 , 0 0 0t o da ya ta na nnua li nt e r e s tr a t eo f6 . 3 5 %, ho w muc hmo ne ywi l ly ouha v ef o ry our da ught e r ' sc o l l e gee duc a t i oni n1 8ye a r s ? A)$ 5 , 6 0 3 B)$ 10 , 0 00 C)$ 1 5, 1 4 4 D)The r ei sn ote no ug hi nf o r ma t i o nt oa ns we rt hi sq ue s t i o n. Answer :C n 1 8=$ Expl anat i on:C)FV=PV∗ ( 1+r ) =$ 5 , 0 0 0∗ ( 1 . 0 63 5) 1 5 , 1 4 4 . 1 5 MODE=END I NPUT 18 6. 3 5 KEY N I /Y CPT 15, 144. 15

5 , 000 PV

0 PMT

? FV



1 8 )Y ouwo nt hes t a t el o t t e r yandt o okt hepa y o uta sa$ 1 , 2 8 3 , 4 7 5l umps um t o da y . Yo urs p ous eha s de c i de dt ha ty oune e dt oi n ve s tt hi smo ne yf o rt hene x t1 0ye a r sa ndc a ne x pe c ti tt oe a r na na v e r a g e a nnua lr a t eo fr e t ur no f7 . 1 8 %. I ft hi sc o me st opa s s ,ho w muc hmo ne ywi l lb ei nt hea c c o unta tt hee ndo f t hep er i o d? A)$ 8, 4 71 , 2 53 B)$ 2, 5 67 , 5 86 C)$ 1, 9 2 0, 3 8 8 D)$ 1, 8 90 , 4 71 Answer :B n 1 0=$ Expl anat i on:B)FV=PV∗ ( 1+r ) =$ 1, 2 83 , 4 75 ,∗ ( 1 . 0 71 8) 2 , 5 6 7 , 5 8 5 . 6 6 MODE=END I NPUT 10 7. 18 KEY N I /Y CPT 2, 567, 585 . 66

1, 283, 475 PV

0 PMT

? FV


1 9 )I fy ouc a ne a r n5 . 2 5 % pe ry e a ro ny ouri n ve s t me nt s , ho wl o ngwi l li tt a k et odo ub l ey o urmo ne y ? A)6 . 3 1ye a r s B)1 9. 0 5ye a r s C)1 3 . 5 5ye a r s D)The r ei sn ote no ug hi nf o r ma t i o nt oa ns we rt hi sq ue s t i o n. Answer :C Expl anat i on:C)n= MODE=END I NPUT ? KEY N CPT 13. 55

= 5. 25 I /Y

=1 3. 5 5ye a r s

1 PV

0 2 PMT FV



2 0)Yourf a t he rs pe nta l lo fhi sa dul tl i f ewor ki ngi nas ma l lT s hi r tma ki ngfir m.Hi sfir s ty e arofs a l e swa s $ 1 1 8, 0 0 0andhi sl a s ty e a ro fs a l e swa s$ 4 5 0 , 0 0 0 .I ft hefir m gr e wa ta na v e r a g er a t eo f3 . 1 5 % pe ry e a r , ho w ma nyy e a r sdi dy ourf a t he rs e l lT s h i r t sa thi sfir m? A)4 3 . 1 6ye a r s B)4 0. 0 0ye a r s C)3 1 . 6 8ye a r s D)2 5 . 9 1ye a r s Answer :A Expl anat i on:A)n= MODE=END I NPUT ? KEY N CPT 43 . 16

3. 1 6ye a r s =4

= 3. 15 I /Y

1 18, 0 00 PV

0 PMT

450, 000 FV


2 1 )Y ourpr o duc t i o nma na g e ri nf o r msy o ut ha tc u r r e n t l yt hefir mi sp r o duc i ng1 , 4 3 8he a t i nguni t sp e r mo nt hb utha sp l a nst oi nc r e a s ep r o duc t i o na tar a t eo f5 % pe rmo nt hunt i lt hefir mi spr o duc i ng3 , 0 0 0 uni t spermont h.How manymont hswi l lt hi st ake? A)27. 33mont hs B)15. 07mont hs C)14mont hs D)The r ei sn ote no ug hi nf o r ma t i o nt oa ns we rt hi sq ue s t i o n. Answer :B Expl anat i on:B)n= MODE=END I NPUT ? KEY N CPT 15. 0 7

= 5 I /Y

=15. 07mont hs

1, 438 PV

0 PMT

3, 000 FV



22)DanPr es t onmade$18, 000i nt hefir s tmovi eheevers t ar r edi n.Dansoonmademor eandmor emovi es andmor eandmor emoney .Ata46. 18% r at eofs al ar yi ncr eas epermovi e, how manymovi esdi dDan ma k ei no r de rt oe a r n$ 5 , 3 5 0 , 0 0 0i nas i ng l emo vi e ? A)84movi es B)34movi es C)22movi es D)15movi es Answer :D Expl anat i on:D)n= MODE=END I NPUT ? KEY N CPT 15

es =15movi

= 46 . 18 I /Y

18, 000 PV

0 PMT

5, 350, 000 FV


2 3)Gi v enat i mepe r i od,a ni nt e r e s tr a t e ,a ndaf ut ur ev a l ue ,ape r s onc o ul ds o l v ef orapr e s e ntva l ue . Ans we r :TRUE Di ff:1 T opi c :3 . 4Appl i c a t i o nso ft heT i meVa l ueo fMo ne yEq ua t i o n AACS B:3An a l y t i c a lThi n ki n g LO:3 . 4Appl yt het i mev a l ueo fmo ne ye qua t i o nus i ngf o r mul a ,c a l c ul a t o r ,a nds p r e a ds h e e t .

2 4 )Y ouha v e$ 5 , 0 0 0i na ni nde xmut ua lf und.Ata na v e r a g ea nnua lr a t eo fr e t ur nof1 0 % pe ry e a r ,t hi s i n ve s t me nts h oul de x c e e dav al ueof$ 5 00 , 0 0 0byt het i mey our e t i r ei n4 0ye a r s . Ans we r :F ALSE n 40 Expl anat i on:FV=PV∗ ( 1+r ) =$ 5 , 0 0 0∗ ( 1 . 1) =$ 2 26 , 2 9 6. 2 8. Di ff:2 T opi c :3 . 4Appl i c a t i o nso ft heT i meVa l ueo fMo ne yEq ua t i o n AACS B:3An a l y t i c a lThi n ki n g LO:3 . 4Appl yt het i mev a l ueo fmo ne ye qua t i o nus i ngf o r mul a ,c a l c ul a t o r ,a nds p r e a ds h e e t .

2 5 )Youwi nt he$ 5, 0 0 0 , 0 0 0l o t t e r yt ha tpa y sy ou$ 2 5 0, 0 0 0pe ry e a ro ve ra2 0y e a rpe r i od.Gi v e nne g at i v e i nt e r e s tr a t e s ,t hel ot t e r yha sapr e s e ntv al uet ha ti sl e s st h an$ 5, 0 00 , 0 00 . Ans we r :F ALSE Ex pl a na t i o n:Youwi nt he$ 5 , 0 0 0, 0 0 0l o t t e r yt ha tpa y sy ou$ 2 5 0, 0 0 0pe ry e a ro v e ra2 0y e a rpe r i o d.Gi v e n ne ga t i v ei nt e r e s tr a t e s , t hel o t t e r yha sapr e s e ntva l uet ha ti sGREATERt ha n$ 5, 0 00 , 0 00 . Di ff:3 T opi c :3 . 4Appl i c a t i o nso ft heT i meVa l ueo fMo ne yEq ua t i o n AACS B:3An a l y t i c a lThi n ki n g LO:3 . 4Appl yt het i mev a l ueo fmo ne ye qua t i o nus i ngf o r mul a ,c a l c ul a t o r ,a nds p r e a ds h e e t .


2 6)I fi nt e r e s tr a t e sa r epos i t i v e,t he ndi s c o unt i ngi nc r e a s e st h ef ut ur ev al ueofa ni nv es t me ntwhi l e compoundi ngr educe st hepr es entval ueofani nvest ment . Ans we r :F ALSE Expl anat i on:Di s c ount i ngDECREASESt hePRESENTval ueofani nves t mentwhi l ec ompoundi ng I NCREASESt heFUTUREval ueofani nve s t ment . Di ff:1 T opi c :3 . 4Appl i c a t i o nso ft heT i meVa l ueo fMo ne yEq ua t i o n AACS B:3An a l y t i c a lThi n ki n g LO:3 . 4Appl yt het i mev a l ueo fmo ne ye qua t i o nus i ngf o r mul a ,c a l c ul a t o r ,a nds p r e a ds h e e t .

2 7 )Apl a ntnur s e r ypa y s$ 2 , 0 0 0f o r8 0 0one g al l onflo we r i ngt r e e s ,pl a nt st he m, a ndf or g e t st he m.F i v e y ea r sl a t e r ,t henur s e r yi sa bl et os e l le ac hoft he1 00t r e e st ha ts ur vi ve df or$ 5 0e ac h.Wha ti st her a t eof r e t ur noni t st ot a li nve s t me nt ? 1/n 1/5 Ans wer :r=( FV/PV) -1=( ( 1 00 * $ 5 0) /$ 2, 0 00 ) -1=2 0. 1 1 % Di ff:3 T opi c :3 . 4Appl i c a t i o nso ft heT i meVa l ueo fMo ne yEq ua t i o n AACS B:3An a l y t i c a lThi n ki n g LO:3 . 4Appl yt het i mev a l ueo fmo ne ye qua t i o nus i ngf o r mul a ,c a l c ul a t o r ,a nds p r e a ds h e e t .

2 8)I fc ol l e get ui t i ona ndf e e si nc r e a s eata na nnua lr a t eof7 % pe ry ea r , a ndy ourl i t t l es i s t e ri sc ur r e nt l y s t a r t i nghe rf r e s hma ny ea ri nhi ghs c h ool ,wha ti st hee xpe c t e dc o s tofhe rfir s ty ea ro fc o l l e gei nf our y e ar si ft ui t i ona ndf e e sa r ec ur r e nt l y$ 6, 8 5 0pe ry e a r ?Ho w muc hf ort hes t a r tofhe rs e ni ory e a ro fc o l l e ge s t a r t i ngt hr e eye ar sa f t e rt ha t ? n 4 Ans wer :FV=PV×( 1+r ) =$ 6 , 8 5 0×( 1 . 0 7 ) =$ 8, 9 78 . 9 5.Thr e ey ea r sl a t e rt heannua lt ui t i onc os ti s $ 1 0 , 9 9 9 . 6 0 . Di ff:3 T opi c :3 . 4Appl i c a t i o nso ft heT i meVa l ueo fMo ne yEq ua t i o n AACS B:3An a l y t i c a lThi n ki n g LO:3 . 4Appl yt het i mev a l ueo fmo ne ye qua t i o nus i ngf o r mul a ,c a l c ul a t o r ,a nds p r e a ds h e e t .

3.& Doubling o! $one%' #"e (ule o! )2 1 )Ke l vi nha s$ 2 , 5 0 0butne e ds$ 5 , 0 0 0t opur c ha s eane w go l fc a r t .I fhec a ni n ve s thi smo ne ya tar a t eof 1 2 % pe ry e a r ,a ppr o x i ma t e l yho w ma n yy e a r swi l li tt a ket hemo ne yi nKe l vi n' sa c c o untt ogr o wt o$ 5, 0 0 0 ? Us et heRul eof72t odet er mi neyouranswer . No t e :Thego l fc a r t ' sp r i c ema yha v ec ha ng e db yt het i meKe l vi n' sa c c o untr e a c he sav a l ueo f$ 5 , 0 0 0 . A)2year s B)4y e ar s C)6y e a r s D)8year s Answer :C Ex pl a na t i o n:C)

=6y e ar svi at heRul eof7 2 .

Di ff:2 T o pi c :3 . 5Do ub l i ngo fMo ne y :Th eRul eo f7 2 AACS B:3An a l y t i c a lThi n ki n g LO:3 . 5Ex pl a i nt heRul eof7 2 ,as i mpl ee s t i ma t i o no fd oub l i ngv a l ue s .


2 )Youc a ni n ve s ty ourmo ne ya tar a t eof7 % pe ry e a r .Att hi sr a t ei twi l lt a key ouj us to ve r_ _ _ _ __ _ _y e a r s t odoubl eyourmoney .Us et heRul eof72t odet er mi neyourans wer . A)4 B)1 0 C)5 . 5 D)The r ei sn ote no ug hi nf o r ma t i o nt oa ns we rt hi sq ue s t i o n. Answer :B Ex pl a na t i o n:B)

=1 0 . 3y e a r svi at heRul eo f7 2 .


3)Whatannualr at eofr et ur nmus tyouear nt odoubl eyourmoneyi nabout9year s ?Us et heRul eof72t o det er mi neyoura nswer . A)Youwoul dneedt oear nanannualr at eofr et ur nofabout12%. B)Youwoul dneedt oear nanannualr at eofr et ur nofabout10%. C)Youwoul dneedt oear nanannualr at eofr et ur nofabout8%. D)The r ei sn ote no ug hi nf o r ma t i o nt oa ns we rt hi sq ue s t i o n. Answer :C Ex pl a na t i o n:C)

=8 % vi at heRul eo f7 2 .


4 )Thedi vi de ndspe rs ha r epa i db yF a nt a s t i c a l l yF i neF er n sI nc . ( FFF)doubl e df r o m as t a r t i ngv al ueof $ 1 . 5 0i n2 0 07t oava l ueof$ 3 . 0 0i n2 0 13( as i x y e arp e r i od) .Wha twa st hea ppr o x i ma t ea v e r a g ea nnua lr a t e o fgr o wt ho fF FF ' sdi vi de ndspe rs h a r e ?Us et heRul eo f7 2t ode t e r mi ney oura ns we r . A)FFF' sdi vi dendsgr ew atanannualr at eofappr oxi mat el y12% peryear . B)F FF ' sd i vi de ndsg r e wa ta na nnua lr a t eo fa ppr o x i ma t e l y10 % pe ry e a r . C)FFF' sdi vi dendsgre w atanannualr at eofappr oxi mat el y8% peryear . D)F FF ' sdi vi de ndsgr e wa ta na nnua lr a t eo fa ppr o x i ma t e l y6 % pe ry e a r . Answer :A Ex pl a na t i o n:A)

=1 2 % vi at heRul eo f7 2 .

Di ff:2 T o pi c :3 . 5Do ub l i ngo fMo ne y :Th eRul eo f7 2 AACS B:3An a l y t i c a lThi n ki n g LO:3 . 5Ex pl a i nt heRul eof7 2 ,as i mpl ee s t i ma t i o no fd oub l i ngv a l ue s . Hmwr kQue s t i o ns :*T a k e nf r o m" Pr e ppi ngf o rE x a ms "q ue s t i o nsa tt h ee ndo ft h ec h ap t e r .


5 )I ny ourfir s ty e a ro uto fc o l l e g ey ouho pet oe a r n$ 6 0 , 0 0 0pe ry e a r . Ho w ma n yy e a r swi l ly ouha v et o wo r kunt i ly oue a r n$ 12 0 , 0 0 0i fy ouri nc o mei nc r e a s e sa tar a t eo f1 0 % pe ry e a r ?Us et heRul eo f7 2t o det er mi neyoura nswer . A)Yo uwo ul dne e dt owo r kf o rj us to v e r5y e a r st or e a c ha ni nc o mel e v e lo f$ 1 0 0 , 0 0 0pe ry e a r . B)Y ouwo ul dne e dt owo r kf o rj us to v e r6y e a r st or e a c hani nc o mel e v e lo f$ 1 0 0 , 0 0 0pe ry e a r . C)Yo uwo ul dne e dt owo r kf o rj us to v e r7y e a r st or e a c hani nc o mel e v e lo f$ 1 0 0 , 0 0 0pe ry e a r . D)Yo uwo ul dne e dt owo r kf o rj us to v e r8y e a r st or e a c ha ni nc o mel e v e lo f$ 1 0 0 , 0 0 0pe ry e a r . Answer :C Ex pl a na t i o n:C)

=7 . 2y e a r svi at heRul eof7 2 .


6 )Ama nuf a c t ur e ro fLCDt e l e vi s i o nsh ass e e ns a l e si nc r e a s ef r om 1 2 5, 0 0 0uni t spe ry e art o50 0 , 0 0 0uni t s pe ry e a ri n8y e ar s . Wha tha sb e e nt hefir m' sa v e r a gea nnua lr a t eo fi nc r e a s ei nt henumbe ro ft e l e vi s i on s e t ss o l d?Us et heRul eo f7 2t ode t e r mi ney oura ns we r . A)Theaver ageannualr at eofchangehasbeenbet wee n10% and11%. B)Theaver ageannualr at eofchangehasbeenbet ween18% and19%. C)Theaver ageannualr at eofc hangehasbee nbet ween15% and16%. D)The r ei sn ote no ug hi nf o r ma t i o nt oa ns we rt hi sq ue s t i o n. Answer :B Ex pl a na t i o n:B)Uni ts a l e sd oubl e df r om 1 2 5, 0 0 0t o2 50 , 0 0 0a nddo ubl e da ga i nt o5 00 , 0 0 0i n8y e a r s .Thus , a tado ubl i ngr a t eo fe v e r yf o ury e a r st heRul eo f7 2s ugg e s t sa na nnua lr a t eo f

=1 8%.Vi at hef or mul a

t hea c t ua lgr o wt hr a t ei s1 8 . 9 2 % pe ry e a r . Di ff:2 T o pi c :3 . 5Do ub l i ngo fMo ne y :Th eRul eo f7 2 AACS B:3An a l y t i c a lThi n ki n g LO:3 . 5Ex pl a i nt heRul eof7 2 ,as i mpl ee s t i ma t i o no fd oub l i ngv a l ue s . Hmwr kQue s t i o ns :*T a k e nf r o m" Pr e ppi ngf o rE x a ms "q ue s t i o nsa tt h ee ndo ft h ec h ap t e r .

7 )TheRul eo f7 2i sar ul eoft humbf o re s t i ma t i ngt hel e ngt ho ft i mene c e s s a r yt odo ub l ey ourmo ne y , gi ve na ni nt e r e s tr a t e . Ans we r :TRUE Di ff:1 T o pi c :3 . 5Do ub l i ngo fMo ne y :Th eRul eo f7 2 AACS B:3An a l y t i c a lThi n ki n g LO:3 . 5Ex pl a i nt heRul eof7 2 ,as i mpl ee s t i ma t i o no fd oub l i ngv a l ue s .

8 )TheRul eof7 2i sar ul eoft humbf ore s t i ma t i ngt hei nt e r e s tr a t ene c e s s a r yt odoub l ey ourmone y , gi v e n ape r i o do ft i me . Ans we r :TRUE Di ff:1 T o pi c :3 . 5Do ub l i ngo fMo ne y :Th eRul eo f7 2 AACS B:3An a l y t i c a lThi n ki n g LO:3 . 5Ex pl a i nt heRul eof7 2 ,as i mpl ee s t i ma t i o no fd oub l i ngv a l ue s .


9 )TheRul eof7 2c a nb eus e dt oqui c k l ye s t i ma t ei nt e r e s tr a t e sn e c e s s a r yt odo ub l ey ourmo ne yi nagi v e n t i mepe r i o dwi t ho utt heus eo fas p r e a ds h e e to rc a l c u l a t o r .Ho we v e r ,t her ul edo e sNOTwo r kf o r e s t i ma t i nggr o wt hr a t e s . Ans we r :F ALSE Ex pl a na t i on:TheRul eof7 2wo r ksf ora nyr a t eofc ha nge ,no tj us ti nt e r e s tr a t er e t ur n s . Di ff:2 T o pi c :3 . 5Do ub l i ngo fMo ne y :Th eRul eo f7 2 AACS B:3An a l y t i c a lThi n ki n g LO:3 . 5Ex pl a i nt heRul eof7 2 ,as i mpl ee s t i ma t i o no fd oub l i ngv a l ue s .

10)Gi venenought i me, youcoul ddoubl eyourmoneywi t hari s kf r eei nvest ment . Ans we r :TRUE Di ff:1 T o pi c :3 . 5Do ub l i ngo fMo ne y :Th eRul eo f7 2 AACS B:3An a l y t i c a lThi n ki n g LO:3 . 5Ex pl a i nt heRul eof7 2 ,as i mpl ee s t i ma t i o no fd oub l i ngv a l ue s .

1 1 )As s umeyouput$ 2 , 0 0 0i nt oat a x f r e ei n ve s t me nta ndl e a v ei tt he r ef o r4 5y e a r sa ta na nnua lr a t eof 8 %. Ac c o r d i ngt ot heRul eof7 2 ,y ouri n ve s t me ntwi l lg r o wt oav al ueofa bo ut$ 6 4 , 0 0 0 . Ans we r :TRUE Ex pl a na t i o n:Ac c o r d i ngt ot heRul eo f7 2 ,a ni n ve s t me nte a r ni ng8 % ay e a rwi l ldo ub l ei nv a l ue a ppr o x i ma t e l ye v e r y9ye a r s .Thus , t he$ 2, 0 0 0wi l lgr o wt oa bout$ 6 4 , 0 0 0i n4 5y e ar s . I n4 5y e ar s , t he ori gi nali nvest mentwi l ldoubl efivet i mes( $2K×2=$4K,$4K×2=$8K,$8K×2=$16K,$16K×2= $32 K,and$32 K×2=$64 K) . Di ff:2 T o pi c :3 . 5Do ub l i ngo fMo ne y :Th eRul eo f7 2 AACS B:3An a l y t i c a lThi n ki n g LO:3 . 5Ex pl a i nt heRul eof7 2 ,as i mpl ee s t i ma t i o no fd oub l i ngv a l ue s .

1 2 )Thet e l e v i s i o nc o mme r c i a lpi t c h ma nt e l l sy o uhec a ndo ub l ey ourmo ne ywi t har i s k f r e ei n ve s t me nti n j us t1 0ye a r s .I ft hi si st r ue ,whati nt e r e s tr a t emus tt hi sr i s k f r e ei nve s t me nte ar nonanannualbas i s ?Sol ve t hi sq ue s t i o nus i ngt heRul eof7 2andt he ni namo r ee x a c tf a s h i o nus i ngaf o r mul a ,y ourc a l c ul a t o r ,or c omput e r .I nt oda y' sr a t ee n vi r o nme nt , i st hei nt e r e s tr a t et ha ty ous ol ve df orar e a l i s t i ca nnua lr a t eof r e t ur nf orar i s k f r e ei nve s t me nt ? Ans we r :Yo ur1 0 y e a rr i s k f r e ei n ve s t me ntwo ul dha v et oe a r na b out7 . 2 0 % pe ry e a rv i at heRul eo f 7 2 ,whe r et her a t ei sde t e r mi ne dbydi vi di ng7 2b yt het i mepe r i o do r

y e a r s=7 . 2 0 %.Amo r ee x a c t

1 /n 1/10 r e s ul ti sf o undvi at hef o r mul ar=( FV/PV) -1=( $ 2 /$ 1 ) -1=7 . 1 8 %. Ast hi spr ob l e mi swr i t t e n, 1 0 y e a rt r e a s ur ybo ndsa r ey i e l di ngc l o s et o2 . 2 5 %,s oana nnua lr a t eof7 . 2 0 % onar i s k f r e ei n ve s t me nti s no tv e r yl i ke l y .Ho we v e r ,t hec o r r e c ta ns we rt ot hi spo r t i o noft heque s t i o nwi l lde pe ndonc ur r e nt e c o no mi cc o ndi t i o ns . Di ff:3 T o pi c :3 . 5Do ub l i ngo fMo ne y :Th eRul eo f7 2 AACS B:3An a l y t i c a lThi n ki n g LO:3 . 5Ex pl a i nt heRul eof7 2 ,as i mpl ee s t i ma t i o no fd oub l i ngv a l ue s .


Chapter 03

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