Question

Ayaan invests a sum of money for 3 years compounded annually. He finds that CI for the second year is ₹ 1260 and ₹ 1323 is the CI for the third year. Calculate the rate of interest and the sum invested by him.

Answer 1

Given, the CI for the second year is ₹ 1260 and for the third year it is ₹ 1323, when it is compounded yearly.

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

= ₹ (1323 – 1260)

= ₹ 63

∴ ₹ 63 is the interest on ₹ 1260 for 1 years.

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

∴ `(1260 xx R xx 1)/100 = 63`

⇒ `R = (63 xx 100)/1260`

⇒ R = 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)^3 - P(1 + 5/100)^2 = 1323`

⇒ `P[(21/20)^3 - (21/20)^2] = 1323`

⇒ `P[9261/8000 - 441/400] = 1323`

⇒ `P[(9261 - 8820)/8000] = 1323`

⇒ `P[441/8000] = 1323`

⇒ `P = (1323 xx 8000)/441`

⇒ P = 24000

Hence, the required rate of interest is 5% and the invested sum is ₹ 24000.