Question

The SI on a certain sum is ₹ 400 for 2 years and the CI on the same sum at the same rate for 2 years is ₹ 410. Find the rate of interest and the sum borrowed.

Answer 1

Given, simple interest on a certain sum is ₹ 400 for 2 years and the compound interest on the same sum at the same rate for 2 years is ₹ 410.

	Simple interest	Compound interest
First year	₹ `400/2` = ₹ 200	₹ 200
Second year	₹ 200	₹ 410 – 200 = ₹ 210

An extra of ₹ 10 is the interest earned in 1 year by 200 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.

∴ `(200 xx R xx 1)/100 = 10`

⇒ `R = (10 xx 100)/200`

⇒ R = 5

The required rate of interest is 5%.

Let the principal be ₹ P.

∴ `(P xx 5 xx 1)/100 = 200`

⇒ `P = (200 xx 100)/5`

⇒ P = 4000

Hence, the rate of interest is 5% and the sum invested is ₹ 4000.