Find the compound interest on Rs. 5000 in 2 years at 4% per annum, the interest being compounded half yearly.

Given:

Principal (P) = ₹5000

Rate (r) = 4% per annum

Time (t) = 2 years

Interest is compounded half-yearly.

Formula used:

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

Where, n = number of times interest is compounded per year (n = 2 for half-yearly)

Calculations:

Rate per half-year (r/n) = 4/2 = 2%

Number of half-years (n × t) = 2 × 2 = 4

A = 5000(1 + \(\frac{2}{100})^4\)

⇒ A = 5000(1.02)⁴

⇒ A = 5000 × 1.08243216 = 5412.16

Compound Interest (CI) = A - P

⇒ CI = 5412.16 - 5000 = 412.16

∴ The correct answer is option (4).