Question

A sum of ₹ 16,000 earns ₹ 1640 as interest in 2 years when compounded annually. Find the rate of interest.

Answer 1

Given:

• Principal (P) = ₹ 16,000 
• Compound Interest (CI) = ₹ 1,640 
• Time (n) = 2 years
• Interest is compounded annually

Compound Interest:

`CI = A - P = P(1 +R/100)^n - P`

`1640 = 16000(1 + R/100)^2 - 16000`

⇒ `1640/16000 = (1 + R/100)^2 - 1`

⇒ `0.1025 = (1 + R/100)^2 - 1`

⇒ `(1 + R/100)^2 = 1.1025`

⇒ `1 + R/100 = sqrt(1.1025)`

⇒ `1 + R/100 = 1.05`

⇒ `R/100 = 1.05 - 1`

⇒ `R/100 = 0.05`

⇒ R = 5%