Correct Answer - Option 4 : Rs.4,532

**Given:**

Amount = 729/625 × Sum

**Formula:**

Let P = principal, R = rate of interest and N = time period

Compound interest (calculated annually) = P(1 + R/100)^{n} - P

Amount(compounded half yearly) = P(1 + (R/2)/100)^{2n}

Let P = Principal, R = R% and N = \(a\dfrac{1}{b}\) years

Compound interest = P(1 + R/100)^{a}{1 + (1/b × R/100)} - P

**Calculation:**

Time = 1 year

⇒ Amount = P(1 + R/200)^{2}

⇒ 729P/625 = P(1 + R/200)^{2}

⇒ (27/25)^{2} = (1 + R/200)^{2}

⇒ 27/25 = 1 + R/200

⇒ R/200 = 2/25

⇒ R = 16%

**∴ Required compound interest = [10000(1 + 16/100)**^{2}{1 + (16/2)/100}] - 10000 = Rs.4532.48 ≈ Rs.4532