Question

The SI on a certain sum for 2 years is ₹ 1200 and the CI on the same sum at the same rate for 2 years is ₹ 1272. Find the rate of interest and the sum invested.

Answer 1

Given, the simple interest on a certain sum for 2 years is ₹ 1200 and the compound interest on the same sum at the same rate for 2 years is ₹ 1272.

	Simple interest	Compound interest
First year	₹ `1200/2` = ₹ 600	₹ 600
Second year	₹ 600	₹ (1272 – 600) = ₹ 672

An extra of ₹ 72 is the interest earned in 1 year by 600 which is added to the principal.

Simple interest = `(P xx R xx T)/100`, where P is the principal, R is the rate of interest and T is the time period

∴ `(600 xx R xx 1)/100 = 72`

⇒ `R = (72 xx 100)/600`

⇒ R = 12

The required rate of interest is 5%.

Let the principal be ₹ P.

∴ `(P xx 12 xx 1)/100 = 600`

⇒ `P = (600 xx 100)/12`

⇒ P = 5000

Hence, the rate of interest is 12% and the sum invested is ₹ 5000.