Question

A sum amounts to ₹ 8820 in 2 years and ₹ 9261 in 3 years compounded annually. Find the rate and the sum.

Answer 1

Given, a sum amounts to ₹ 8820 in 2 years and ₹ 9261 in 3 years compounded annually.

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

= ₹ 9261 – 8820

= ₹ 441

∴ ₹ 441 is the interest on ₹ 8820 for 1 year.

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

∴ `(8820 xx R xx 1)/100 = 441`

⇒ `R = (441 xx 100)/8820`

⇒ 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 = 8820`

⇒ `P(1 + 1/20)^2 = 8820`

⇒ `P(21/20)^2 = 8820`

⇒ `P = (8820 xx 20 xx 20)/(21 xx 21)`

⇒ P = 8000

Hence, the required sum and the rate of interest are ₹ 8000 and 5% respectively.