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.