On a sum of Rs 2500 for 2 years, the compound interest (compounded annually) is Rs 16 more than the simple interest at the same rate. Find the rate of interest per annum.
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 8%
For 2 years the compound interest exceeds the simple interest only by the interest on the first year’s interest, which is \(\displaystyle P\left(\frac{r}{100}\right)^{2}\).
\(\displaystyle 2500\times\left(\frac{r}{100}\right)^{2}=16\)
\(\displaystyle \left(\frac{r}{100}\right)^{2}=\frac{16}{2500}\), so \(r^{2}=\displaystyle\frac{16\times10000}{2500}=64\)
\(r=8\)
The rate is 8% per annum.
Why the other options are incorrect
Option (1) 9% — Incorrect. At 9% the gap is \(\displaystyle 2500\times\left(\frac{9}{100}\right)^{2}=20.25\), not Rs 16.
Option (2) 4% — Incorrect. At 4% the gap is \(\displaystyle 2500\times\left(\frac{4}{100}\right)^{2}=4\), not Rs 16.
Option (3) 6% — Incorrect. At 6% the gap is \(\displaystyle 2500\times\left(\frac{6}{100}\right)^{2}=9\), not Rs 16.