I borrowed ₹12,000 at 6% per annum on simple interest for 2 years. Had I borrowed the sum at 6% per annum on compound interest for the same duration, then what extra amount would I have paid as interest?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → ₹43.20
Simple interest is the same every year, but compound interest in the second year is also charged on the first year’s interest; that is the whole of the extra amount.
Simple interest for 2 years \(\displaystyle =\frac{12000\times6\times2}{100}=1440\)
Amount at compound interest \(=12000\times(1.06)^{2}=12000\times1.1236=13483.20\)
Compound interest \(=13483.20-12000=1483.20\)
Extra interest \(=1483.20-1440=43.20\), that is, ₹43.20
Shortcut: For 2 years, CI − SI \(\displaystyle =P\left(\frac{r}{100}\right)^{2}\), the interest on the first year’s interest.
\(12000\times(0.06)^{2}=12000\times0.0036=43.20\)