A sum invested at 10% p.a. for 2 years becomes ₹ 3,267, when the interest is…

Concept

For the same principal (P) and rate (R), Compound Interest (CI) over n years follows Amount = P(1 + R/100)ⁿ, while Simple Interest (SI) over any time T follows SI = (P × R × T) / 100 — SI grows linearly with time, unlike CI.

Application

1. The amount becomes ₹3,267 in 2 years at R = 10% p.a. compounded annually, so 3,267 = P × (1 + 10/100)² = P × (1.1)².

2. (1.1)² = 1.21, so P = 3,267 / 1.21 = ₹2,700.

3. Using this same principal and rate, apply the simple-interest formula for 2½ years: SI = (P × R × T) / 100 = (2,700 × 10 × 2.5) / 100.

4. SI = 67,500 / 100 = ₹675.

Cross-check

Compounding ₹2,700 forward confirms the given data: after year 1 it grows to 2,700 × 1.1 = ₹2,970, and after year 2 to 2,970 × 1.1 = ₹3,267 — matching the amount stated in the question. Separately, the simple interest for one year on ₹2,700 at 10% is ₹270, and 270 × 2.5 = ₹675, confirming the result.