A sum of money amounts to Rs. 7719.8 at the rate of 10% compounded annually…

Concept: For compound interest, the amount after n years is A = P × (1 + r/100)n, where P is the principal, r is the annual rate (in percent), and n is the number of years the sum is compounded. To find the principal when the amount is known, rearrange the formula as P = A ÷ (1 + r/100)n.

Application:

1. Substitute the known values: A = 7719.8, r = 10%, n = 3, so the growth factor is (1 + 10/100)3 = (1.1)3.

2. Compute the growth factor: (1.1)3 = 1.1 × 1.1 × 1.1 = 1.331.

3. Divide the amount by the growth factor to get the principal: P = 7719.8 ÷ 1.331 = 5800.

Cross-check:

Multiplying the principal back by the growth factor confirms the result: 5800 × 1.331 = 7719.8, which matches the given amount.

Hence, the sum of money is Rs. 5800.