What is the compound interest on a sum of Rs. 12,000 at 20% p.a for \(2\frac{3}{4}\) years, interest compounded annually?

Given:

Principal amount = Rs. 12000

Rate of interest = 20%

Time = \(2\frac{3}{4}\) years

Concept used:

In case of the compound interest,

Amount = P(1 + R/100)^N

CI = P(1 + R/100)^N - P

where

P = Principal amount

R = Rate of interest per year

N = Time in years

Calculation:

The compound interest on a sum of Rs. 12,000 at 20% p.a for \(2\frac{3}{4}\) years

⇒ 12000(1 + 20/100)²(1 + \({{{3 \over 4} × {20}} \over 100}\)) - 12000

⇒ 17280 × 1.15 - 12000

⇒ Rs. 7,872

∴ The compound interest on a sum of Rs. 12,000 at 20% p.a for \(2\frac{3}{4}\) years, interest compounded annually is Rs. 7,872.