# compound interest

1. A bank offers 5% compound interest calculated on half-yearly basis. A customer deposits Rs. 1600 each on 1st January 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

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.

C.I. = Rs. (3321 – 3200) = Rs. 121

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

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.

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

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.

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

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

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

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.