# Compound Interest - Aptitude Questions and Answers - RejinpaulPlacement

36.
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? [R.B.I. 2003]

Solution:   [15000 * {1 + (R/100)}^2 - 15000] - [(15000 * R * 2)/100] = 96
=> 15000 [{1 + (R/100)}^2 - 1 - (2R/100)] = 96
=> 15000[{(100 + R)^2 - 10000 - 200R}/10000] = 96
=> R^2 = [(96 * 2)/3] = 64
=> R = 8%
37.
The difference between simple and compound interest compounded annually on a certain sum of money for 2 years at 4% per annum is Re. 1. The sum (in Rs.) is: [S.S.C. 2003]

Solution:   Let the sum be Rs. x. Then,

C.I. = [x {1 + (4/100)}^2 - x] = [(676/625)x - x] = (51/625)x.

S.I. = [(x * 4 * 2)/100] = 2x/25

(51x/625) - (2x/25) = 1
=> x = 625
38.
The compound interest on a sum of money for 2 years is Rs. 832 and the simple interest on the same sum for the same period is Rs. 800. The difference between the compound interest and the simple interest for 3 years will be:

Solution:   Difference in C.I. and S.I. for 2 years = Rs. 32.

S.I. for one year = Rs. 400
S.I for Rs. 400 for one year = Rs. 32.

So, Rate = [(100 * 32)/(400 * 1)] % = 8%

Hence, difference in C.I. and S.I for 3rd year
= S.I. on Rs. 832
= Rs. [(832 * 8 * 1)/100] = Rs. 66.56

Total difference = Rs. (32 + 66.56) = Rs. 98.56
39.
The difference between the simple interest on a certain sum at the rate of 10% per annum for 2 years and compound interest which is compounded every 6 months is Rs. 124.05. What is the principal sum? [S.B.I.P.O. 2000]

Solution:   Let the sum be Rs. P. Then,

P[{1 + (5/100)}^4 - 1] - [(P * 10 * 2)/100] = 124.05
=> P[(21/20)^4 - 1 - (1/5)] = 124.05
=> P[(194481/160000) - (6/5)] = 12405/100
=> P[(194481 - 192000)/160000] = 12405/100
=> P = [(12405/100) * (160000/2481)] = 8000
40.
The difference between compound interest and simple interest on a sum for 2 years at 10% per annum, when the interest is compounded annually is Rs. 16. If the interest were compounded half-yearly, the difference in two interests would be:

Solution:   For first year, S.I. = C.I.

Now, Rs. 16 is the S.I. on S.I. for 1 year.
Rs. 10 is S.I. on Rs. 100.

Rs. 16 is S.I.on Rs.[(100/10) * 16] = Rs. 160
So, S.I. on principal for 1 year at 10% is Rs. 160.

Principal = Rs. [(100 * 160)/(10 * 1)] = Rs. 1600

Amount for 2 years compounded half yearly = Rs. [1600 * [1 + (5/100)]^4 ] = Rs. 1944.81.

C.I. = Rs. (1944.81 - 1600) = Rs. 344.81

S.I. = Rs. [(1600 * 10 * 2)/100] = Rs. 320

C.I. - S.I = Rs. (344.81 - 320) = Rs. 24.81
41.
A sum of money lent at compound interest for 2 years at 20% per annum would fetch Rs. 482 more, if the interest was payable half-yearly than if it was payable annually. The sum is:

Solution:   Let the sum be Rs. x. Then,

C.I. when compounded half-yearly = [x * {1 + (10/100)}^4 - x] = (4641/10000)x

C.I. when compounded annually = [x * [1 + (20/100)]^2 - x] = (11/25)x

(4641/10000)x - (11/25)x = 482
=> x = [(482 * 10000)/241] = 20000
42.
On a sum of money, the simple interest for 2 years is Rs. 660, while the compound interest is Rs. 696.30, the rate of interest being the same in both the cases. The rate of interest is: [Hotel Management, 1997]