A sum of ₹10,000 becomes ₹14,400 on compound interest in 2 years. What is the rate of interest per annum?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 20%
Under compound interest the amount after \(n\) years is \(P\left(1+\displaystyle\frac{r}{100}\right)^n\), so the ratio of amount to principal is a perfect square here.
Amount after 2 years: \(10000\left(1+\displaystyle\frac{r}{100}\right)^2=14400\)
Dividing by the principal: \(\left(1+\displaystyle\frac{r}{100}\right)^2=1.44\)
Taking the square root (\(1.2^2=1.44\)): \(1+\displaystyle\frac{r}{100}=1.2\), so the rate is 20% per annum