The difference between the amounts of compound interest and simple interest on the same amount invested at the same rate for 2 years is Rs. 32. If the interest rate is 4% per annum, calculate the amount invested (in Rs.).
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 20,000
In the first year compound and simple interest are equal. In the second year compound interest also earns interest on the first year's interest, which is \(P\times\frac{r}{100}\times\frac{r}{100}\). So for 2 years the difference between the two is \(P\left(\frac{r}{100}\right)^2\).
Putting in the difference of Rs. 32 and the rate of 4%: \(32=P\times\left(\frac{4}{100}\right)^2=P\times\frac{16}{10000}\)
The amount invested is \(\displaystyle P=\frac{32\times10000}{16}=20000\) rupees