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1.	A bank offers 5% compound interest calculated on half-yearly basis. A customer deposits Rs. 1600 each on 1 January and 1 July of a year. At the end of the year, the amount he would have gained by way of interest is:
Answer» 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:
Answer» 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?
Answer» 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?
Answer» 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.	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.?
Answer» 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

6.	The least number of complete years in which a sum of money put out at 20% compound interest will be more than doubled is:
Answer» 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.

7.	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?
Answer» Amount = Rs. 8000 x 1 + 5 2 100 = Rs. 8000 x 21 x 21 20 20 = Rs. 8820.

8.	The effective annual rate of interest corresponding to a nominal rate of 6% per annum payable half-yearly is:
Answer» 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%

9.	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:
Answer» 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

10.	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?
Answer» 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 C.I. = Rs. (551.25 - 500) = Rs. 51.25

11.	The difference between simple interest and compound on Rs. 1200 for one year at 10% per annum reckoned half-yearly is:
Answer» 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.

12.	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?
Answer» 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%.

13.	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:
Answer» 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

14.	The compound interest on Rs. 30,000 at 7% per annum is Rs. 4347. The period (in years) is:
Answer» 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.

15.	At what rate of compound interest per annum will a sum of Rs. 1200 become Rs. 1348.32 in 2 years?
Answer» 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%