CHS08 - General Mathematics GBS FOR WEEK NO. 13 ! "0 S#$$lementar% E&ercises '. Cm$lete the the ta(le (% cm$#tin) cm$#tin) !r #n*n+n #n*n+n ,al#es. ,al#es. n n#m(ers n#m(ers 3 / an r#n r#n 2 %#r ans+er t si& ecimal $laces. Nminal nterest Fre#enc% nterest Rate E#i,alent Rate $er Rate cm$#ne ! $er 4eri Nminal $eri Cn,ersin Rate (ase n 4eris rate an $eri !rm $re,i#s cl#mn 105 #arterl% 617 6"7 637 697 cm$#ne semiann#all% /5 semi" 6:7 6/7 6;7 ann#all% cm$#ne mnthl% 1"5 mnthl% 1" 687 67 6107 cm$#ne #arterl% 1st r+< Nminal Rate
nterest cm$#ne
Fre#enc% ! Cn,ersin 4eris
105
=#arterl% 63 mnths7
3
nterest Rate $er 4eri
0.1 4 > 0.0": > ".:5
E#i,alent Nminal Rate
10.381"5 cm$#ne semiann#all%
Rate $er $eri (ase n rate an $eri !rm $re,i#s cl#mn 10.381" 5
Gi,en< e#al 4? e#al t 105 cm$#ne #arterl% i697 > 0.1 m>9 4 t 5 cm$#ne semi-ann#all% i6"7 > @ m>" 4 t Aet F1 (e the !#t#re ,al#e +hen interest is cm$#ne semi-ann#all% an F " (e the !#t#re ,al#e +hen interest is 105 cm$#ne #arterl%. F1 > F" (4 )
i 4 t 1+ ¿ 4 (2 ) i (2 )t 1 + ¿ = P ¿ 2 P ¿
0.1 4 ¿ 4 i( 2 ) ( 1 + )=¿ 2 1+
i6i7 > 61.0":79 1 i6"7 > 0.10381" > 10.381"5 'ns+er< 10.381"5 cm$#ne semi-ann#all%
"n r+< Nminal Rate
nterest cm$#ne
Fre#enc% ! Cn,ersin 4eris
nterest Rate $er 4eri
E#i,alent Nminal Rate
Rate $er $eri (ase n rate an $eri !rm $re,i#s cl#mn /.05
/5 Semi" /.05 0.06 cm$#ne ann#all% cm$#ne > 2 6/ mnths7 semimnthl% ann#all%? i6"7 0.03 > 35 > 0.0/ Gi,en< e#al 4? e#al t /5 cm$#ne semi-ann#all% i6"7 > 0.0/ m>" 4 t 5 cm$#ne mnthl% i61"7 > @ m > 1" 4 t Aet F1 (e the !#t#re ,al#e +hen interest is cm$#ne mnthl% an F " (e the !#t#re ,al#e +hen interest is /5 cm$#ne semi-ann#all%. F1 > F" (2 )
i 2 t 1+ ¿ 2 ( 12 ) i ( 12) t 1 + ¿ = P ¿ 12 P ¿ 0 . 06 2 ¿ 2 i( 12 ) ( 1 + )=¿ 12 1+
i6i7 > 61.037" 1 i61"7 > 0.0/0 > /.05 'ns+er< /.05 cm$#ne mnthl% 3r r+< Nminal nterest Fre#enc%
nterest
E#i,alent
Rate $er
Rate
cm$#ne
! Cn,ersin 4eris
1"5 cm$#ne mnthl%? i61"7 > 0.1"
Mnthl% 61" mnths7
1"
Rate $er 4eri
0.12 12 >
Nminal Rate
1"./8":5 cm$#ne #arterl%
$eri (ase n rate an $eri !rm $re,i#s cl#mn 1"./8": 5
0.01 > 15 Gi,en< e#al 4? e#al t 1"5 cm$#ne mnthl% i61"7 > 0.1" m > 1" 4 t 5 cm$#ne #arterl% i697 > @ m>9 4 t Aet F1 (e the !#t#re ,al#e +hen interest is cm$#ne #arterl% an F " (e the !#t#re ,al#e +hen interest is 1"5 cm$#ne mnthl%. F1 > F" 1
1
+
0.12
+
12 t
¿
12
( )
i4 4
¿ ( ) t = P ¿ 4
P ¿ 1
+
0.12
(1 +
12 ( 4)
i
4
12
¿
)=¿
i6i7 > 61.0171" 1 i697 > 0.1"/8": > 1"./8":5 'ns+er< 1"./8":5 cm$#ne mnthl%
B. Cm$lete the ta(le (% nin) the #n*n+n time an rate.
1st r+<
1
1.:1;5 =#arterl% 8000
0.3; 5 0.;;9 5 1.18: 5 1./01" 5 ".00:: 5 ".9119 5 ".818 5 3.""81 5 3./38 5 9.0:13 5 9.9/:3 5 9.8815
1
"
3
:."89 5 :.;1;9 5 /.1385 "
3
/.:/09 5 /.899 5 ;.9101 5 ;.83;: 5 8."//; 5 8./;: 5 .135 .:/93 5 10.0003 5
9
:
/
1
31.83
"
/3.;
3
:.88
9
1"8.1
:
1/0.99
/
1".1
;
"":.:"
8
":8.":
"1.11
10
3"9.1
11
3:;.""
1"
30.98
13
9"3.8;
19
9:;.3
1:
91.09
1/
:"9.83
1;
::8.;:
18
:".81
1
/";
"0
//1.33
"1
/:.8
"" "3
;30.9 ;/:.19
"9
800.0"
8031.8 3 80/3.; 80:.8 8 81"8.1 81/0.9 9 81". 1 8"":.: " 8":8." : 8"1.1 1 83"9.1 83:;." " 830.9 8 89"3.8 ; 89:;.3 891.0 9 8:"9.8 3 8::8.; : 8:".8 1 8/"; 8//1.3 3 8/:.8 8;30.9 8;/:.1 9 8800.0 "
"n r+<
115 Semi;:000 1
"
:.:5 11.30": 5 1;.9"91 5 "3.88": 5 30.//5 3;.8893 5 9:.9/; 5 :3.9/8; 5 /1.09 5 ;0.8199 5 80."0" 5 0.1"0; 5 100.:;; 95 111./0 15 1"3."9; /5 13:.:"/ 35
1
1 " 3
"
9
3
: / ;
9
8
:
10 11
/
1" 13
;
19 1:
8
1/
91": 89;/.8 8 130/8. 1 1;11. 8: "30"" "8913. "1 39100. 9 90101. 9 9/93". 0; :3110. 83 /01:/. 3 /;:0. :/ ;:933. 09 83;0/. 8/ "93:. ;9 101/9 9.;
;1": 839;/.8 8 880/8.1 "11.8 : 80"" 103913. "1 10100. 9 11:101. 9 1"193". 0; 1"8110. 83 13:1:/. 3 19":0. :/ 1:0933. 09 1:8;0/. 8/ 1/;93:. ;9 1;//99. ;
C. Sl,e the !ll+in) $r(lems< "1. D#n in,este an am#nt ! ₱100000 +here he (taine an interest ! ₱1/000 at the en ! " %ears. 't +hat nminal rate cm$#ne semi-ann#all% +as it in,este@ Gi,en< F > ₱100000 4 > ₱1/000 t > ".: %ears m>" n > mt > 6"76".:7 > : Fin< i6"7 Sl#tin< F > 4617n 100000 > 1/000 61 7 : 5
+ j ¿
1
100000 16000 5
+ j ¿ 6.25=¿ 1
=¿
6.25 ¿
6.25 ¿
1 5
=1 + j ¿ 1 5
−1= 0.4426 ¿
j = 0.4426 i
(¿¿ 2 ) m j =¿
i
(¿¿ 2 ) 2 0.4426 =¿ i6"7 > 60.99"/76"7 i6"7 > 0.88:" r 88.:"5
"".Den in,este an am#nt ! ₱900000 at :5 cm$#ne #arterl%. H+ ln) sh#l she let the in,estment sta% i! she +ants t earn ₱:0000@ (4)
Given : F =400,000 P=50,000 i
=0.12 m=4 j =
(4 )
i 0.12 = = 0.03 m 4
Fin< t Sl#tin< F > 4617n 900000 > :000061 0.037 n
log
(
)=
400,000 50,000
n log ( 1.03)
400000 ) 50000 =70.3493 periods log ( 1.03 )
log ( n= t =
n 70.3493 = =17.58 year s m 4
"3. Mr. Retanan +as )i,en a lan at 105 cm$#ne mnthl%. When sh#l he $a% it s that it +ill #st earn nl% 105 ! the am#nt (rr+e@
( 12)
Given : i( c )=0.1 P F =1.2 P i
( 12 )
=0.1 m=12 j =
i
m
=
0.1 12
= 0.0083333333333333
0.008333
Fin< t Sl#tin< F > 4617n 1."4 > 461 0.0083337n 1." > 61.0083337 n l)61."7 > l)61.0083337 n l)61."7 > n l)1.0083337
n= t =
log 1.2 =21.97 periods log ( 1.008333)
n 21.97 = =5.49 year s m 4
"9.'t +hat interest rate cm$#ne #arterl% sh#l an am#nt (e in,este i! the interest earne is "05 ! the in,este am#nt !r : %ears@ ":.What sim$le interest rate is e#i,alent t 15 cm$#ne #arterl%@ (4)
Given : i
=0.01m =4 t =5 years
Fin< r Sl#tin< Sim$le nterest
Cm$#n nterest
F s
P ( 1+ r s t )
>
( 1 +r s t )
>
1+
F c
>
(i)4 4
¿4 t
1+
>
¿
S#(stit#te t > : 4
( 1 +r s )
( 1 +r s ) rs
1
>
>
+
(i) 4
4
¿
¿ 1+
> 0.0100 r 15
0.01 4 ¿ 4
¿
(i)4 m P ¿
¿4 t
