The difference between compound interest and simple interest on a sum for 2 years at 20% per annum, when the interest is compounded annually is ₹32. If the interest were compounded half-yearly, the difference in two interests would be:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → ₹51.28
Over two years, compound interest exceeds simple interest only by the interest earned on the first year’s interest, so CI − SI \(=P\left(\frac{r}{100}\right)^{2}\). This gives the sum; the half-yearly case is then worked out from it, with half the rate for twice the number of periods.
The sum (the difference is the given ₹32):
\(P\times(0.2)^{2}=32\), so \(0.04P=32\)
The sum is \(P=\) ₹800
Compounded half-yearly (10% per half-year, 4 half-years):
Amount after 2 years: \(800\times1.1^{4}=800\times1.4641=1171.28\)
Compound interest, the amount less the sum: \(1171.28-800=371.28\)
Simple interest for 2 years at 20%: \(800\times0.2\times2=320\)
Difference between the two interests: \(371.28-320=\) ₹51.28