The simple interest on a sum of money for 3 years at 6(2/3)% per annum is Rs…

Concept

For simple interest, SI = (P × R × T) / 100, so the principal can be recovered from SI when R and T are known. For compound interest on the same P, R, T compounded annually, the amount grows by a fixed factor (1 + R/100) applied once per year, so CI = P × [(1 + R/100)T − 1] — never just T times the simple-interest rate.

Step-by-step Application

1. Convert the rate 6(2/3)% to an improper fraction: 6(2/3)% = 20/3% per annum.

2. Use the SI formula to find the principal: SI = P × R × T / 100 → 6750 = P × (20/3) × 3 / 100 = P/5, so P = Rs 33,750.

3. Apply the CI formula for 3 years at the same rate: CI = P × [(1 + R/100)3 − 1] = 33750 × [(1 + 20/300)3 − 1] = 33750 × [(16/15)3 − 1].

4. Expand (16/15)3 = 4096/3375, so CI = 33750 × (4096 − 3375)/3375 = 33750 × 721/3375 = Rs 7210.

Cross-check

Verify year by year on the same principal: Year 1 interest = 33750 × 20/300 = Rs 2250 (new balance Rs 36,000); Year 2 interest = 36000 × 20/300 = Rs 2400 (new balance Rs 38,400); Year 3 interest = 38400 × 20/300 = Rs 2560. Total CI = 2250 + 2400 + 2560 = Rs 7210 — matching the formula result.