Ms. Hema invests Rs. 8000 for six months at 20% per annum compounded…

Concept

Compound interest grows a principal by a fixed rate in every compounding period, and each period's interest is earned on the balance that already includes the earlier interest (interest on interest). If a principal P earns a per-period rate i for n periods, the maturity amount is A = P(1 + i)n. When an annual rate R is compounded k times a year, the per-period rate is i = R/k and the number of periods is n = k times the time in years.

Working

1. Per-quarter rate: the annual rate is 20% compounded quarterly, so i = 20% / 4 = 5% = 0.05 per quarter.

2. Number of periods: 6 months equals 2 quarters, so n = 2.

3. Set up the formula: A = 8000 × (1 + 0.05)2 = 8000 × (1.05)2.

4. Evaluate the growth factor: (1.05)2 = 1.1025.

5. Multiply: A = 8000 × 1.1025 = 8820, that is Rs. 8820.

Cross-check

Check it quarter by quarter: after the first quarter, 8000 × 1.05 = 8400; after the second, 8400 × 1.05 = 8820. For contrast, plain simple interest for six months would give only 8000 + 8000 × 0.20 × 0.5 = 8800; the extra Rs. 20 is the second quarter's interest on the first quarter's Rs. 400 of interest (400 × 5% = 20), which is exactly what compounding adds.