# What is the difference between the compound interests on Rs. 10,000 for $2 \frac 1 2$ years at 10% per annum compounded yearly and half-yearly?

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What is the difference between the compound interests on Rs. 10,000 for $2 \frac 1 2$ years at 10% per annum compounded yearly and half-yearly?

1. Rs. 57.81
2. Rs. 65
3. Rs. 70
4. Rs. 60

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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.