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 Answer: Option B 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 Answer: Option A 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 Answer: Option C 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 Answer: Option A 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 Answer: Option A 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.