Question

A sum amounts to ₹ 6600 in 1 year and ₹ 7986 in 3 years at compound interest. Find the rate and the sum.

Answer 1

Given, a sum amounts to ₹ 6600 in 1 year at compound interest.

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 + R/100)^1 = 6600`  ...(1)

The sum amounts to ₹ 7986 in 3 years at compound interest.

∴ `P(1 + R/100)^3 = 7986`  ...(2)

Dividing equation (2) by equation (1), we get

 `(P(1 + R/100)^3)/(P(1 + R/100)) = 7986/6600`

⇒ `((1 + R/100)^3)/((1 + R/100)) = 1.21`

⇒ `(1 + R/100)^(3 - 1) = 1.21`

⇒ `(1 + R/100)^2 = 1.21`

⇒ `1 + R/100 = sqrt(1.21)`

⇒ `1 + R/100 = 1.1`

⇒ `R/100 = 1.1 - 1`

⇒ `R/100 = 0.1`

⇒ `R = 0.1 xx 100`

⇒ `R = 10`

Again, `P(1 + 10/100)^1 = 6000`

⇒ `P(1 + 1/10) = 6600`

⇒ `P(11/10) = 6600`

⇒ `P = (6600 xx 10)/11`

⇒ `P = 6000`

Hence, the rate of interest and the sum are 10% and ₹ 6000.