Correct Answer - Option 1 : Rs. 57.81

**Given:**

Principal = 10000

Time = \(2 \frac 1 2\) = 5/2 years

Rate of Interest = 10%

**Formula:**

Amount = P(1 + R/100)^{n}

For half yearly

Amount = P(1 + R/200)^{2n}

Here, P = Principal, R = Rate, n = Time

**Calculations:**

Amount when interest compounded yearly = 10000(1 + 10 /100)^{2} (1 + 0.5 × 10/100)

⇒ 10000(11/10)(11/10)(21/20)

⇒ Rs. 12705

CI = 12705 – 10000 = Rs. 2705

Amount when interest compounded half-yearly = 10000(1 + 5 /100)^{5}

⇒10000(21/20)^{5}

⇒Rs 12762.81

CI = 12762.81 – 10000 = 2762.81

⇒ Difference = 2762.81 – 2705

⇒ Rs. 57.81

**∴**** Difference between interest compounded yearly and half yearly is Rs. 57.81.**