A principal amount of ₹8,000 is invested at an annual interest rate of 5% compounded half-yearly. What will be the compound interest earned after 4 years? [Use 1.025)⁸= 1.2184]

Given:

Principal amount (P) = ₹8,000

Annual interest rate (R) = 5%

Compounding frequency = half-yearly

Time (T) = 4 years

Formula Used:

Amount (A) for compound interest compounded half-yearly = \(P \left(1 + \frac{R/2}{100}\right)^{2T}\)

Compound Interest (CI) = A - P

Calculation:

The half-yearly interest rate and the total number of compounding periods.

Rate per half-year (r) = R / 2 = 5% / 2 = 2.5%

Number of compounding periods (n) = 2T = 2 × 4 = 8 periods

\(A = P \left(1 + \frac{r}{100}\right)^{n}\)

\(A = 8000 \left(1 + \frac{2.5}{100}\right)^{8}\)

\(A = 8000 (1 + 0.025)^{8}\)

\(A = 8000 (1.025)^{8}\)

A = 8000 × 1.2184

A = 9747.2

CI = A - P

CI = 9747.2 - 8000

CI = 1747.2

∴ The compound interest earned after 4 years is ₹1747.20.