Question

A certain sum amounts to ₹ 26,460 in 2 years and ₹ 27,783 in 3 years when compounded annually. Calculate the rate of interest and the sum borrowed.

Answer 1

Given, a certain sum amounts to ₹ 26,460 in 2 years and ₹ 27,783 in 3 years when compounded annually.

Compound interest for 1 year = Amount after 3 years – Amount after 2 years

= ₹ (27,783 – 26,460)

= ₹ 1,323

∴ ₹ 1,323 is the interest on ₹ 26,460 for 1 year.

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.

∴ `(26,460 xx R xx 1)/100 = 1,323`

⇒ `R = (1,323 xx 100)/(26,460)`

⇒ `R = 5`

The required rate of interest is 5%.

Amount = `P(1 + R/100)^T`, where P is the principal, R is the rate of interest and T is the time period.

⇒ `P(1 + 5/100)^2 = 26,460`

⇒ `P(21/20)^2 = 26,460`

⇒ `P = (26,460 xx 20 xx 20)/(21 xx 21)`

⇒ `P = 24,000`

Hence, the required sum and the rate of interest are ₹ 24,000 and 5% respectively.