# Compound Interest - Aptitude Questions and Answers - RejinpaulPlacement

43.
The effective annual rate of interest corresponding to a nominal rate of 6% per annum payable half-yearly is:

Solution:   Amount of Rs. 100 for 1 year when compounded half-yearly
= Rs. [100 * {1 + (3/100)}^2 ] = Rs. 106.09

Effective rate = (106.09 - 100)% = 6.09 %
44.
A person lent out a certain sum on simple interest and the same sum on compound interest at a certain rate of interest per annum. He noticed that the ratio between the difference of compound interest and simple interest of 3 years and that of 2 years is 25 : 8. The rate of interest per annum is:

Solution:   Let the principal be Rs. P and rate of interest be R% per annum .

Difference of C.I and S.I. for 2 years.
= [P * {1 + (R/100)}^2 - P] - {(P * R * 2)/100] = PR^2/104

Difference of C.I. and S.I. for 3 years
= [P * {1 + (R/100)}^3 - P] - [(P * R * 3)/100] = (PR^2/10^4)[(300 + R)/100]

[(PR^2/10^4)[(300 + R)/100] / (PR^2/10^4) ] = 25/8
=> [(300 + R)/100] = 25/8
=> R = 100/8 = 12   1/2 %
45.
Mr. Dua invested money in two schemes A and B offering compound interest@ 8 p.c.p.a. and 9 p.c.p.a. respectively. If the total amount of interest accrued through two schemes together in two years was Rs. 4818.30 and the total amount invested was Rs. 27,000, what was the amount invested in Scheme A? [Bank P.O. 2003]

Solution:   Let the investments in scheme A be Rs. x.
Then, investment in scheme B = Rs. (27000 - x)

[x * {[1 + (8/100)]^2 - 1} + (27000 - x){[1 + (9/100)]^2 - 1}] = 4818.30
=> [x * (104/625)] + {[1881(27000 - x)]/10000 } = 481830/100
=> 1664x + 1881(27000 - x) = 48183000
=> (1881x - 1664x) = (50787000 - 48183000)
=> 217x = 2604000
=> x = (2604000/217) = 12000
46.
A sum of money invested at compound interest amounts to Rs. 800 in 3 years and to Rs. 840 in 4 years. The rate of interest per annum is: [S.S.C. 2001]

Solution:   S.I on Rs. 800 for 1 year = Rs. (840 - 800) = Rs. 40

Rate = [(100 * 40)/(800 * 1)] = 5%
47.
A sum of money invested at compound interest amounts to Rs. 4624 in 2 years and to Rs. 4913 in 3 years. The sum is :

Solution:   S.I on Rs. 4624 for 1 year = Rs. (4913 - 4624) = Rs. 289

Rate = [(100 * 289)/(4624 * 1)] = 6 1/4 %

Now, x [ 1 + 25/(4 * 100)]^2 = 4624
=> x * (17/16) * (17/16) = 4624
=> x = [4624 * (16/17) * (16/17)] = Rs. 4096
48.
A sum of Rs. 12,000 deposited at compound interest becomes double after 5 years. After 20 years, it will become:

Solution:   12000 * [1 + (R/100)]^5 = 24000
=> [1 + (R/100)]^5 = 2

[{1 + (R/100)}^5]^4 = 2^4 = 16
=> [1 + (R/100)]^20 = 16
=> P[1 + (R/100)]^20 = 16P
=> 12000 [1 + (R/100)]^20 = 16 * 12000 = 192000
49.
A sum of money placed at compound interest doubles itself in 5 years. It will amount to eight times itself at the same rate of interest in: [Hotel Management, 2003]