The compound interest compounded annually on a sum of Rs. 15625 in three years…

CONCEPT

For annual compounding, the amount after n years is A = P(1 + r/100)n. Compound interest is A - P, so when P and the interest are known, first find A and then compare A/P with the multi-year growth factor.

APPLICATION

1. Principal P = 15625 and compound interest = 4058, so amount A = 15625 + 4058 = 19683.

2. Use A/P = (1 + r/100)3 = 19683/15625.

3. Recognize 19683 = 273 and 15625 = 253, so 19683/15625 = (27/25)3.

4. Therefore 1 + r/100 = 27/25 = 1.08, giving r/100 = 0.08 and r = 8%.

CROSS-CHECK

At 8%, A = 15625 × 1.083 = 15625 × 1.259712 = 19683, so the interest is 19683 - 15625 = 4058.

Result: the annual rate of interest is 8%.