A sum of money lent out at simple interest amounts to Rs. 720 after 2 years…

Concept: In simple interest the interest accrued is the same every year, so the interest for any span of time equals the yearly interest times the number of years. Between two amounts of the same loan, the rise in amount over a period is purely the interest for that period, and the rate is the yearly interest as a fraction of the principal: r = (yearly interest ÷ principal).

Application:

1. The amount grows from Rs. 720 to Rs. 1020 over the further 5 years, so the interest for those 5 years is 1020 − 720 = Rs. 300.

2. Because each year earns the same simple interest, the yearly interest is 300 ÷ 5 = Rs. 60.

3. The Rs. 720 after 2 years is principal plus 2 years' interest: P + 2 × 60 = 720, so P + 120 = 720, giving the principal P = Rs. 600.

4. Rate r = yearly interest ÷ principal = 60 ÷ 600 = 0.10 = 10% per annum.

Cross-check: At 10% on Rs. 600 the yearly interest is Rs. 60. After 2 years the amount is 600 + 120 = Rs. 720, and after 7 years it is 600 + 7 × 60 = 600 + 420 = Rs. 1020 — both given figures match, confirming the rate.

Result: The rate of interest is 10% per annum.