# Compound Interest - Aptitude Questions and Answers - RejinpaulPlacement

22.
What is the difference between the compound interest on Rs. 5000 for 1   1/2 years at 4% per annum compounded yearly and half-yearly? [S.S.C. 2000]

Solution:   C.I. when interest is compounded half-yearly
= Rs. [5000 * {1 + (4/100)} * [1 + [((1/2) * 4)/100]]]
= Rs. [5000 * (26/25) * (51/50)]
= Rs. 5304

C.I. when interest is compounded half-yearly
= Rs. [5000 * {1 + (4/100)}^3 ]
= Rs. [5000 * (51/50) * (51/50) * (51/50)]
= Rs. 5306.04

Difference = Rs. (5306.04 - 5304) = Rs. 2.04
23.
Find the compound interest on Rs. 15,625 for 9 months at 16% per annum compounded quarterly. [R.R.B. 2002]

Solution:   P = Rs. 15625, n = 9 months = 3 quarters, R = 16% p.a. = 4% per quarter.

Amount = Rs. [15625 * {1 + (4/100)}^3]
= Rs. [15625 * (26/25) * (26/25) * (26/25)]
= Rs. 17576

C.I. = Rs. (17576 - 15625) = Rs. 1951
24.
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 rate and for the same time? [C.B.I. 1997]

Solution:   Sum = Rs. [(50 * 100)/(2 *5)] = Rs. 500

Amount = Rs. [500 * {1 + (5/100)}^2 ]
= Rs. [500 * (21/20) * (21/20)]
= Rs. 551.25

C.I. = Rs. (551.25 - 500) = Rs. 51.25
25.
What will be the difference between simple and compound interest @ 10% per annum on a sum of Rs. 1000 after 4 years? [Bank P.O. 2002]

Solution:   S.I = Rs. [(1000 * 10 * 4)/100] = Rs. 400

C.I. = Rs. [1000 * {1 + (10/100)}^4 - 1000] = Rs. 464.10

Difference = Rs. (464.10 - 400) = Rs. 64.10
26.
The difference between simple interest and compound interest on Rs. 1200 for one year at 10% per annum reckoned half-yearly is: [R.R.B. 2002]

Solution:   S.I. = Rs. [(1200 * 10 * 1)/100] = Rs. 120

C.I. = Rs. [1200 * {1 + (5/100)}^2 - 1200] = Rs. 123

Difference = Rs. (123 - 120) = Rs. 3
27.
The compound interest on Rs. 30,000 at 7% per annum is Rs. 4347. The period (in years) is: [L.I.C.A.A.O. 2003]

Solution:   Amount = Rs. (30000 + 4347) = Rs. 34347

Let the time be n years. Then,

30000 [1 + (7/100)]^n = 34347
=> (107/100)^n = 34347/30000 = 11449/10000 = (107/100)^2

n = 2 years.
28.
At what rate of compound interest per annum will a sum of Rs. 1200 become Rs. 1348.32 in 2 years?