CDC Department University
Simple & Compound Interest
SRM
1. Simple interest on an amount after 36 months at the rate of 3% per quarter is 720. The amount is 1) 4000
2) 2000
Exp: SI = PRT =720= 100
3) 6000
P ×3 × 100
36 4
4) 4800
=¿ P=2000
Note: R is 3% per quarter, so 36 months is 36/4…. 2. An amount becomes 8,800 in four years at 15% p.a. What is that amount? 1) 5,500
2)7,500
3) 5,800
4) 6,400
Exp: Amount becomes 8800, So Principal+ SI=8800, P+SI=
P=
P+
PRT RT 4 × 15 3 8 =P 1+ =P 1+ =P 1+ = P=8800 100 100 100 5 5
(
) (
) ( )
8800× 5 =5500 8
3. Amir took a loan of 900 at the rate of 12% per year for 8 months. How much does he need to pay at the end of 8 months? 1) 952
2) 852
900× 12× Exp: SI=
100
8 12
3) 872
4) 972
=72 (Time usually calculate per year, so 8 months= 8/12)
Amount paid= Principal+ SI= 900+72=972 4. The simple interest on a sum of money will be 900 after 3 years. In the next 3 years if principal is doubled, then what will be the total interest at the end of the 6 th year? 1) 900
2) 1800
3) 2700
4) 3600
Exp: SI after 3 years 900. We know that SI always constant every year…. After 3rd year the principal is double. So, SI also doubles, then next 3 years 900*2=1800 Total after 6 years 900+1800=2700
CDC Department University
Simple & Compound Interest
SRM
5. If 40000 is given as loan for a period of 3 years with interest rates 5%, 7% and 9% for the 1st, 2nd and 3rd years respectively, what is the total amount that needs to be paid in the end? 1) 23500
2) 24200
3) 18000
4) 24000
Exp: 6. Ganesh borrowed some money at the rate of 5% p.a. for the first three years, 7% p.a. for the next 5 years and 9% p.a. for the period beyond eight years. If the total interest paid by him at the end of 14 years is 6240, how much money did he borrow? 1) 6300
3) 6200
4) 6000
( P ×1005× 3 + P ×7100×5 + P×1009 ×6 )=6240
Exp:
P
2) 6180
15 35 54 6240× 100 + + =6240=¿ P= =6000 ( 100 100 100 ) 104
7. A sum of money becomes 1120 in 4 years and 1360 in 7 years at SI. How much money is deposited? 1) 900
2) 700
3) 800
4) 1200
Exp: We know that SI always constant every year… So, Difference 7year – 4 year is 3 year= 1360-1120= 240 is SI of money in 3 years Then SI for 1 year is 240/3= 80, for 4 years 4*80= 320 A sum of money becomes 1120 in 4 years, Principal = Amount – SI= 1120-320=800 8. Arun borrows 1500 from two money lenders. He pays interest at the rate of 12% per annum for one loan and at the rate of 14% pa for the other. How much does he borrow at 12% pa if the total interest paid at the end of the year is 186? 1) 1200
2) 1125
3) 1250
4) 1800
Exp: Let assume two amounts is X at 12% and 1500-X at 14%.
SI =
12 X 100
and
SI =
Total interest is 186=
( 1500−X ) 14 14 X =210− 100 100 12 X 100 +
210−
14 X 100 =
2X 24 ×100 =24, X = =1200 100 2
CDC Department University
Simple & Compound Interest
SRM
9. A sum amounts to 3 times itself at SI in 5 years. In what time will it become 5 times itself? 1) 5 years
2) 15 years 3) 10 years
4) 7.5 years
Exp: Let Principal is P, then Amount =3P in 5 years. So, SI for 5 years is Amount-P= 3P-P=2P
¿ Then 2P
P × R ×5 , Rate of interest is 40% per year. 100
So, 5 times means Amount=5P, then SI=4P
4 P=
Then,
P × 40 ×T , Time =10 years. 100
Short cut {based on SI only}: Let p=100, Amt=300 in 5 years so SI=200 100
SI=200, Amt= 300 5 years
SI= 400, Amt=500 10 years
SI=600, Amt= 700 15 years
SI=800, Amt= 900
Principa 20 years l SI is constant value, so it doubles in 5 yr means, 4 times in next 5 yrs. 10. What will be the compound interest on 15000 for 2 years at 12% per annum? 1) 3604
Exp:
2) 3816
1+ R/100 ¿ ¿ CI =P¿
CI =15000(1+
3) 3836
4) 3800
and CI=Principal + Interest
12 2 112 2 ) =15000×( ) =18816 100 100
Then, Interest Amt = 18816-15000=3816 11. Compound interest on a certain amount for 2 years at the rate of 5% is 102.5. Find the amount. 1) 500
2) 725
Exp: Interest= CI-P=>
P{(1+
3) 850
5 2 ) −1 }=102.5 100
Simplify, P{(1.05×1.05)-1}=102.5 => P(1.1025-1)=102.5
4) 1000
CDC Department University
Simple & Compound Interest
SRM
P=102.5/ 0.1025= 1000 12. An amount of 10000 is taken as loan by Ajmal at compound interest charging 8% p.a. for 1st year and 9% p.a. for the 2nd year. How much is the total to be paid by Ajmal after 2 years? 1) 16000
2) 14772
3) 12000
4) 11772
108 109 × Exp: CI Amount= 10000( 100 100 ) = 11772 13. A sum of 40000 is invested for 18 months at 20% p.a. on compound interest. If the interest is compounded half yearly, what will be the interest to be paid? 1) 13240
2) 13080
3) 13530
4) 13540
) R /2 2 n 20/ 2 2 ( 18 (1+ ) =40000(1+ ) 12 Exp: CI Amt calculate half yearly = P 100 100
Amount= 53240, interest= 53240-40000= 13240. 14. Rohit has given a loan to Sohit an amount of 20000 at an interest rate 8 % p.a. for a period of 30 months. If interest charged is at compound interest, how much does Sohit need to pay in the end? 1) 23000 Exp:
2) 24000.36 3) 24261.12
20000 ×
108 108 104 × × 100 100 100
4) 25020.54
= 24261.12
(1+ 1008 )= 108 100
(Note:
For 6 months R= 8/2=4%.... so 104/100 15. A sum of money invested at CI amounts to 800 in 3 years, 882 in 5 years. Find the rate of interest? 1) 2.5% Exp:
Solve
2) 5%
3) 4%
3
4) 6.66%
5
R R P 1+ =800 → 1.∧P 1+ =882→ 2. 100 100
(
2÷ 1
)
=>
(
(
2
1+
)
2
R 882 441 21 = = = So , Cancel t h e square∈bot h side . 100 800 400 20
)
( )
CDC Department University
Simple & Compound Interest
SRM
100+ R 21 = solve R=5 100 20 16. On a given amount the compound interest at the end of first year was 81 and the second year was 88.29. How much money was invested? 1) 900 Exp:
2) 996
(
P 1+
3) 880
4) Cannot be determined
R 1 R 2 =81 →1.∧P 1+ =88.29 →2. 100 100
)
(
)
solve R=9 per annum . (1+ 100R )= 88.79 81
Solve 2÷ 1 =>
(
P{ 1+
Interest on CI for 1 year =
❑ 9 −1}=81 100
)
Solve P=Rs. 900 Note: These kinds of problems go with options… 17. A sum of 5000 is invested for 3 years at 5% p.a. on compound interest. Income Tax at the rate of 20% on the interest earned was deducted at the end of each year. The amount at the end of 3rd year? 1) 5624.32 2) 5630.50
3) 5620.54
4) 5608.30
Exp: Interest for 1 year 5% of 5000= 250 5% of 5200= 260 5% of 5208= 260.4 Amount= 5000+ 200+ 208
Tax 20% of 250=50 20% of 260=52 20% of 260.4=52.08 + 208.32= 5616.32
Amount 250-50=200 260-52=208 260.4-52.08= 208.32
18. A sum of money doubles itself at CI in 9 years. In how many years will it become 16 times itself? 1) 18 years 2) 36 years Exp:
3) 27 years 4) 45 years
R 9 R n P 1+ =2 P →1, P 1+ =16 P →2 100 100
(
)
(
)
CDC Department University
Solve 2 ÷ 1=>
Simple & Compound Interest
(
1+
SRM
R n R 9 16 24 ÷ 1+ = = 100 100 2 2
) (
)
n =4. So ,n=36 years .{Power values are equal } 9 Short cut {based on CI only}: Let P = 100, after 9 years 200. Final amount = 1600 100 Basic
200 9 years
400 18 years
800 27 years
1600 36 years
19. What is the difference between compound interest and simple interest for the sum of 20000 over a 2 year period, if CI is calculated at 20% p.a. and SI is calculated at 23% p.a.? 1) 200
2) 125
Exp: SI for 2 years,
CI for 2 years,
3) 250
20000 ×
(
20000 1+
4) 400
23 ×2=9200 100 2
20 =28800. Interest is 8800 100
)
Diff is 9200-8800=400 20. If the difference between the simple interest and compound interest on some amount at 10% pa for 3 years is 372, then what must be the principal amount? 1) 12400
2) 12000
3) 14800
4) 18000
Exp: Diff b/w CI & SI is PCI−PSI=P((1+R/100)^n −(1+nR/100))
10 3 3 ×10 (1+ ) −(1+ )} = P{ 100 100 P=372/0.031= 12000
P{(1.1)3−1.3 }=372=¿ P(1.331−1.3)=0.031 P=372
