Ms. Shivangi invests Rs. 4000 for six months at 20% per annum compounded…

Concept

When interest is compounded more than once a year, the annual rate is split across each compounding period and applied repeatedly. The compound-amount formula is A = P(1 + i)n, where i is the rate per compounding period (annual rate ÷ number of periods per year) and n is the total number of compounding periods over the time span. "Compounded quarterly" means interest is added every 3 months, so each period is one quarter.

Application

1. Per-quarter rate: the 20% annual rate is divided across 4 quarters, so i = 20 ÷ 4 = 5% = 0.05 per quarter.

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

3. Apply the formula: A = 4000 × (1 + 0.05)2 = 4000 × (1.05)2.

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

5. Final amount: A = 4000 × 1.1025 = 4410.

Cross-check

Build it quarter by quarter as an independent check. After the first quarter: 4000 × 1.05 = 4200. After the second quarter: 4200 × 1.05 = 4410. The two-step growth matches the formula result of 4410.