Question

On what sum of money will the difference between the compound interest and simple interest for 2 years be equal to ₹ 25 if the rate of interest charged for both is 5% p.a.?

Answer 1

Rate of interest, R = 5%

Simple interest, `SI = (P xx 2 xx 5)/100`

`CI = P(1 + 5/100)^2 - P`

The difference between CI and SI.

`P(1 + 5/100)^2 - P - (P xx 2 xx 5)/100 = 25`

`P(1 + 1/20)^2 - P - P/10 = 25`

`P[(21/20)^2 - 1 - 1/10] = 25`

`P(441/400 - 1 - 1/10) = 25`

`P((441 - 400 - 40)/400) = 25`

`P((441 - 440)/400) = 25`

`P(1/400) = 25`

P = 100 × 25

P = 10000

∴ The sum of money is ₹ 10000