Question

In what time will ₹ 15,000 yield ₹ 4,965 as compound interest at 10% p.a., compounded annually?

Answer 1

We are given:

• Principal (P) = ₹ 15,000 
• Compound Interest (CI) = ₹ 4,965 
• Rate (R) = 10% per annum 
• Interest is compounded annually
• We need to find the time (n years).

Step 1: Use the CI formula:

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

⇒ `4,965 = 15,000(1 + 10/100)^n - 15,000`

⇒ 4,965 = 15,000 (1.1ⁿ – 1)

⇒ `(4,965)/(15,000) = 1.1^n - 1`

⇒ 0.331 = 1.1ⁿ – 1

⇒ 1.1ⁿ = 1.331

Now solve for n:

log(1.1ⁿ) = log(1.331)

nlog(1.1) = log(1.331)

`n = (log(1.331))/(log(1.1)) = 0.1236/0.0414` ≈ 2.99 ≈ 3 years