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.