On a sum of Rs 6400 for 2 years, the compound interest (compounded annually) is Rs 36 more than the simple interest at the same rate. Find the rate of interest per annum.
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 7.5%
For 2 years the compound interest exceeds the simple interest only by the interest on the first year’s interest, which is \(\displaystyle P\left(\frac{r}{100}\right)^{2}\).
\(\displaystyle 6400\times\left(\frac{r}{100}\right)^{2}=36\)
\(\displaystyle \left(\frac{r}{100}\right)^{2}=\frac{36}{6400}\), so \(r^{2}=\displaystyle\frac{36\times10000}{6400}=56.25\)
\(r=7.5\)
The rate is 7.5% per annum.
Why the other options are incorrect
Option (2) 6.25% — Incorrect. At 6.25% the gap is \(\displaystyle 6400\times\left(\frac{6.25}{100}\right)^{2}=25\), not Rs 36.
Option (3) 9% — Incorrect. At 9% the gap is \(\displaystyle 6400\times\left(\frac{9}{100}\right)^{2}=51.84\), not Rs 36.
Option (4) 6% — Incorrect. At 6% the gap is \(\displaystyle 6400\times\left(\frac{6}{100}\right)^{2}=23.04\), not Rs 36.