Question

At a certain rate, a sum becomes\(\dfrac{729}{625}\) of itself in one year when interest is compounded half yearly. What will be the compound interest on Rs. 10,000 for \(2\dfrac{1}{2}\) years at the same rate of interest, if interest is compounded annually (correct to the nearest rupee)?
1. Rs.4,693
2. Rs.4,352
3. Rs.14,352
4. Rs.4,532

Answer 1

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