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The difference between the compound and the simple interest on a sum for 2 years at 10% per annum, when the interest is compounded annually, is ₹ 28. If the interest were compounded halfyearly, the difference in the two interests will be
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- ₹ 44
- ₹ 28.35
- ₹ 43.41
- ₹ 43.29
Correct Option: C
Given that , Difference = C.I. - S.I. = ₹ 28 , Time = 2 years , Rate = 10%
If the difference between compound interest and simple interest at the rate of r% per annum for 2 years be ( C.I. - S.I. ) , then
| Principal = ( C.I. - S.I. ) |  |  | 2 | |
| r |
| Principal = 28 | | | 2 | = ₹ 2800 | |
| 10 |
If the interest is compounded half yearly, then
| ⇒ r = | = 5% , Time = 4 half years | |
| 2 |
| ∴ Simple interest = | ||
| 100 |
| Simple interest = | = ₹ 560 | |
| 100 |
| Compound interest = 2800 |  |  | 1 + | | 4 | − 1 |  | |
| 100 |
Compound interest = 2800 [1.2155 – 1]
Compound interest = 2800 × 0.2155 = 603.41
∴ Difference = Compound interest - Simple interest
∴ Difference = ₹ (603.41 – 560) = ₹ 43.41
