Ms. Smita invests Rs. 2000 for six months at 20% per annum compounded…

Concept

For compound interest, the maturity amount is A = P(1 + i)n, where P is the principal, i is the interest rate per compounding period (not per year), and n is the number of compounding periods. When interest is compounded quarterly, the annual rate is divided by 4 to get the rate per quarter, and the number of periods is the number of quarters in the term.

Application

1. Rate per quarter: the annual rate is 20%, compounded quarterly, 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 = 2000 x (1 + 0.05)2 = 2000 x (1.05)2.

4. Evaluate the power: (1.05)2 = 1.1025.

5. Multiply: A = 2000 x 1.1025 = 2205.

Cross-check

Build it quarter by quarter: after Q1, 2000 x 1.05 = 2100; after Q2, 2100 x 1.05 = 2205. Both routes give the same maturity value of Rs. 2205. Note that simple interest would give 2000 + 2000 x 0.20 x 0.5 = 2200, so the extra Rs. 5 is the interest-on-interest from compounding.