After 2 years, the ratio between the compound interest obtained from scheme A and B is 99:115 respectively. The total initial investment of both of the schemes (A and B) together is Rs. 70500. The compound interest obtained from scheme C after 2 years at the rate of 25% per annum is Rs. 25312.5. The initial investment of scheme A is 10% less than the initial investment of scheme C. If the rate of interest in scheme B is 30%, then find out the rate of interest in scheme A. In each of the schemes interest is compounded annually.

Solution

The compound interest obtained from scheme C after 2 years at the rate of 25% per annum is Rs. 25312.5.

Let’s assume the initial investment of scheme C is ‘c’.

25312.5 = c of 125% of 125% - c

25312.5 = 1.5625c - c

25312.5 = 0.5625c

c = 45000

The initial investment of scheme A is 10% less than the initial investment of scheme C.

initial investment of scheme A = (100-10)% of 45000

= 90% of 45000

= 40500

The total initial investment of both of the schemes (A and B) together is Rs. 70500.

initial investment of scheme B = 70500-40500 = 30000

After 2 years, the ratio between the compound interest obtained from scheme A and B is 99:115 respectively. If the rate of interest in scheme B is 30%.

interest from scheme B after 2 years = 30000 of 130% of 130% - 30000

= 50700 - 30000

= 20700

interest from scheme A after 2 years = (20700/115)x99 = 17820

Let’s assume the rate of interest in scheme A is ‘r’.

17820 = 40500 of (100+r)% of (100+r)% - 40500

17820 = 40500 [(100+r)% of (100+r)% - 1]

0.44 = [(100+r)% of (100+r)% - 1]

(100+r)% of (100+r)% = 1.44

(100+r) (100+r) = 14400

So the rate of interest in scheme A = r = 20%