Find the compound intrest on ₹20,000 at 20% p.a for 1\(\frac{1}{2}\) years compounded half yearly.

Given:

Principal (P) = ₹20,000

Annual rate of interest (R) = 20% per annum

Time (n) = 1\(\frac{1}{2}\) years = 1.5 years

Interest is compounded half-yearly.

Formula Used:

When interest is compounded half-yearly:

Rate per half-year (r) = R / 2 = 20% / 2 = 10%

Number of half-year periods (t) = n × 2 = 1.5 × 2 = 3

Amount (A) = \(P(1 + \frac{r}{100})^t\)

Compound Interest (CI) = Amount (A) - Principal (P)

Calculation:

Rate per half-year (r) = 10%

Number of half-year periods (t) = 3

Amount (A) = \(20000(1 + \frac{10}{100})^3\)

A = \(20000(1 + 0.10)^3\)

A = \(20000(1.10)^3\)

A = \(20000 \times 1.1 \times 1.1 \times 1.1\)

A = \(20000 \times 1.331\)

A = ₹26,620

Compound Interest (CI) = Amount (A) - Principal (P)

CI = ₹26,620 - ₹20,000 = ₹6,620

The compound interest on ₹20,000 at 20% p.a for 1\(\frac{1}{2}\) years compounded half-yearly is ₹6,620.