A sum of ₹1,00,000 is invested for 1 year at 10% per annum, compounded…

Concept

When interest is compounded more than once a year, convert the annual rate into the rate per compounding period and count the total number of periods.

The amount is A = P(1 + r/m)mt, and compound interest is CI = A − P, where P is the principal, r is the annual rate in decimal form, m is the number of compounding periods per year, and t is time in years.

Application

1. Here P = ₹1,00,000, r = 10/100 = 0.10, m = 2, and t = 1.

2. The half-yearly rate is r/m = 0.10/2 = 0.05, so the rate per half-year is 5%. The number of periods is mt = 2 × 1 = 2.

3. A = 1,00,000(1 + 0.05)2 = 1,00,000 × 1.1025 = ₹1,10,250.

4. CI = A − P = 1,10,250 − 1,00,000 = ₹10,250.

Cross-check

The first half-year earns ₹5,000. The second half-year earns 5% of ₹1,05,000, which is ₹5,250. Their sum is ₹10,250, confirming the result.