If the difference between the compound and simple interest on a certain sum of money for 3 years at 5% per annum is ₹15.25, then find the sum.
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → ₹ 2,000
Compound interest earns interest on interest, while simple interest does not, so the two differ only by the interest earned on earlier interest. For 3 years this difference is \(\displaystyle P\left(\frac{r}{100}\right)^{2}\left(3+\frac{r}{100}\right)\).
With \(r=5\), the difference is \(\displaystyle P\times\frac{1}{400}\times\frac{61}{20}\), and the question gives it as 15.25
So the sum is \(\displaystyle P=\frac{15.25\times8000}{61}\)
This gives \(P=\) ₹2,000