# Compound Interest

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Compound Interest

1. Let Principal = P, Rate = R% per annum, Time = n

1. When interest is compound Annually:
 Amount = P 1 + R n 100
1. When interest is compounded Half-yearly:
 Amount = P 1 + (R/2) 2n 100
1. When interest is compounded Quarterly:
 Amount = P 1 + (R/4) 4n 100
1. When interest is compounded Annually but time is in fraction, say 3
 Amount = P 1 + R 3 x 1 + R 100 100
1. When Rates are different for different years, say R1%, R2%, R3% for 1st, 2ndand 3rd year respectively.
 Then, Amount = P 1 + R1 1 + R2 1 + R3 . 100 100 100
1. Present worth of Rs. xdue n years hence is given by:
Present Worth = x .
 1 + R 100

Questions:

Level-I:

1. A bank offers 5% compound interest calculated on half-yearly basis. A customer deposits Rs. 1600 each on 1stJanuary and 1st July of a year. At the end of the year, the amount he would have gained by way of interest is:
 A. Rs. 120 B. Rs. 121 C. Rs. 122 D. Rs. 123

2. The difference between simple and compound interests compounded annually on a certain sum of money for 2 years at 4% per annum is Re. 1. The sum (in Rs.) is:
 A. 625 B. 630 C. 640 D. 650

3. There is 60% increase in an amount in 6 years at simple interest. What will be the compound interest of Rs. 12,000 after 3 years at the same rate?
 A. Rs. 2160 B. Rs. 3120 C. Rs. 3972 D. Rs. 6240 E. None of these

4. What is the difference between the compound interests on Rs. 5000 for 1 years at 4% per annum compounded yearly and half-yearly?
 A. Rs. 2.04 B. Rs. 3.06 C. Rs. 4.80 D. Rs. 8.30

5. The compound interest on Rs. 30,000 at 7% per annum is Rs. 4347. The period (in years) is:
A. 2
B.
 2 1 2
C. 3
D. 4
6. What will be the compound interest on a sum of Rs. 25,000 after 3 years at the rate of 12 p.c.p.a.?
 A. Rs. 9000.30 B. Rs. 9720 C. Rs. 10123.20 D. Rs. 10483.20 E. None of these

7. At what rate of compound interest per annum will a sum of Rs. 1200 become Rs. 1348.32 in 2 years?
 A. 6% B. 6.5% C. 7% D. 7.5%

8. The least number of complete years in which a sum of money put out at 20% compound interest will be more than doubled is:
 A. 3 B. 4 C. 5 D. 6

9. Albert invested an amount of Rs. 8000 in a fixed deposit scheme for 2 years at compound interest rate 5 p.c.p.a. How much amount will Albert get on maturity of the fixed deposit?
 A. Rs. 8600 B. Rs. 8620 C. Rs. 8820 D. None of these

10. The effective annual rate of interest corresponding to a nominal rate of 6% per annum payable half-yearly is:
 A. 6.06% B. 6.07% C. 6.08% D. 6.09%

11.

Level-II:

Simple interest on a certain sum of money for 3 years at 8% per annum is half the compound interest on Rs. 4000 for 2 years at 10% per annum. The sum placed on simple interest is:

 A. Rs. 1550 B. Rs. 1650 C. Rs. 1750 D. Rs. 2000

12. If the simple interest on a sum of money for 2 years at 5% per annum is Rs. 50, what is the compound interest on the same at the same rate and for the same time?
 A. Rs. 51.25 B. Rs. 52 C. Rs. 54.25 D. Rs. 60

13. The difference between simple interest and compound on Rs. 1200 for one year at 10% per annum reckoned half-yearly is:
 A. Rs. 2.50 B. Rs. 3 C. Rs. 3.75 D. Rs. 4 E. None of these

14. The difference between compound interest and simple interest on an amount of Rs. 15,000 for 2 years is Rs. 96. What is the rate of interest per annum?
 A. 8 B. 10 C. 12 D. Cannot be determined E. None of these

15. The compound interest on a certain sum for 2 years at 10% per annum is Rs. 525. The simple interest on the same sum for double the time at half the rate percent per annum is:
 A. Rs. 400 B. Rs. 500 C. Rs. 600 D. Rs. 800

16.

 What is the rate of compound interest? I. The principal was invested for 4 years. II. The earned interest was Rs. 1491.
 A. I alone sufficient while II alone not sufficient to answer B. II alone sufficient while I alone not sufficient to answer C. Either I or II alone sufficient to answer D. Both I and II are not sufficient to answer E. Both I and II are necessary to answer

17.
 What will be compounded amount? I. Rs. 200 was borrowed for 192 months at 6% compounded annually. II. Rs. 200 was borrowed for 16 years at 6%.
 A. I alone sufficient while II alone not sufficient to answer B. II alone sufficient while I alone not sufficient to answer C. Either I or II alone sufficient to answer D. Both I and II are not sufficient to answer E. Both I and II are necessary to answer

18.
 An amount of money was lent for 3 years. What will be the difference between the simple and the compound interest earned on it at the same rate? I. The rate of interest was 8 p.c.p.a. II. The total amount of simple interest was Rs. 1200.
 A. I alone sufficient while II alone not sufficient to answer B. II alone sufficient while I alone not sufficient to answer C. Either I or II alone sufficient to answer D. Both I and II are not sufficient to answer E. Both I and II are necessary to answer

Level-I:

Explanation:

Amount
 = Rs. 1600 x 1 + 5 2 + 1600 x 1 + 5 2 x 100 2 x 100
 = Rs. 1600 x 41 x 41 + 1600 x 41 40 40 40
 = Rs. 1600 x 41 41 + 1 40 40
 = Rs. 1600 x 41 x 81 40 x 40
= Rs. 3321.
• I. = Rs. (3321 – 3200) = Rs. 121

Explanation:

Let the sum be Rs. x. Then,

 C.I. = x 1 + 4 2 – x = 676 x – x = 51 x. 100 625 625

 S.I. = x x 4 x 2 = 2x . 100 25

 51x – 2x = 1 625 25
• x= 625.

Explanation:

Let P = Rs. 100. Then, S.I. Rs. 60 and T = 6 years.

 R = 100 x 60 = 10% p.a. 100 x 6

Now, P = Rs. 12000. T = 3 years and R = 10% p.a.

C.I.
 = Rs. 12000 x 1 + 10 3 – 1 100
 = Rs. 12000 x 331 1000
= 3972.

Explanation:

C.I. when interest
compounded yearly
 = Rs. 5000 x 1 + 4 x 1 + x 4 100 100
 = Rs. 5000 x 26 x 51 25 50
= Rs. 5304.

C.I. when interest is
compounded half-yearly
 = Rs. 5000 x 1 + 2 3 100
 = Rs. 5000 x 51 x 51 x 51 50 50 50
= Rs. 5306.04

Difference = Rs. (5306.04 – 5304) = Rs. 2.04

Explanation:

Amount = Rs. (30000 + 4347) = Rs. 34347.

Let the time be n years.

 Then, 30000 1 + 7 n = 34347 100

 107 n = 34347 = 11449 = 107 2 100 30000 10000 100

n = 2 years.

Explanation:

Amount
 = Rs. 25000 x 1 + 12 3 100
 = Rs. 25000 x 28 x 28 x 28 25 25 25
= Rs. 35123.20

C.I. = Rs. (35123.20 – 25000) = Rs. 10123.20

Explanation:

Let the rate be R% p.a.

 Then, 1200 x 1 + R 2 = 1348.32 100

 1 + R 2 = 134832 = 11236 100 120000 10000

 1 + R 2 = 106 2 100 100

 1 + R = 106 100 100

R = 6%

Explanation:

 P 1 + 20 n > 2P 6 n > 2. 100 5

 Now, 6 x 6 x 6 x 6 > 2. 5 5 5 5

So, n = 4 years.

Explanation:

Amount
 = Rs. 8000 x 1 + 5 2 100
 = Rs. 8000 x 21 x 21 20 20
= Rs. 8820.

Explanation:

 Amount of Rs. 100 for 1 year when compounded half-yearly = Rs. 100 x 1 + 3 2 = Rs. 106.09 100

Effective rate = (106.09 – 100)% = 6.09%

Explanation:

C.I.
 = Rs. 4000 x 1 + 10 2 – 4000 100
 = Rs. 4000 x 11 x 11 – 4000 10 10
= Rs. 840.

 Sum = Rs. 420 x 100 = Rs. 1750. 3 x 8

Explanation:

 Sum = Rs. 50 x 100 = Rs. 500. 2 x 5

Amount
 = Rs. 500 x 1 + 5 2 100
 = Rs. 500 x 21 x 21 20 20
= Rs. 551.25
• I. = Rs. (551.25 – 500) = Rs. 51.25

Explanation:

 S.I. = Rs 1200 x 10 x 1 = Rs. 120. 100

 C.I. = Rs. 1200 x 1 + 5 2 – 1200 = Rs. 123. 100

Difference = Rs. (123 – 120) = Rs. 3.

Explanation:

 15000 x 1 + R 2 – 15000 – 15000 x R x 2 = 96 100 100

 15000 1 + R 2 – 1 – 2R = 96 100 100

 15000 (100 + R)2 – 10000 – (200 x R) = 96 10000

 R2 = 96 x 2 = 64 3

R = 8.

Rate = 8%.

Explanation:

Let the sum be Rs. P.

 Then, P 1 + 10 2 – P = 525 100

 P 11 2 – 1 = 525 10

 P = 525 x 100 = 2500. 21

Sum = Rs . 2500.

 So, S.I. = Rs. 2500 x 5 x 4 = Rs. 500 100

Explanation:

Let Principal = Rs. P and Rate = R% p.a. Then,

 Amount = Rs. P 1 + R 4 100

 C.I. = P 1 + R 4 – 1 100

 P 1 + R 4 – 1 = 1491. 100

Clearly, it does not give the answer.

Explanation:

 I. Amount = Rs. 200 x 1 + 6 16 100

 II. Amount = Rs. 200 x 1 + 6 16 100

Thus, I as well as II gives the answer.

Explanation:

Given: T = 3 years.

1. gives: R = 8% p.a.
2. gives: S.I. = Rs. 1200.

Thus, P = Rs. 5000, R = 8% p.a. and T = 3 years.

Difference between C.I. and S.I. may be obtained.

So, the correct answer is (E).

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