At what rate of compound interest per annum, a sum of Rs 1800 becomes…

The correct answer is Option (4) → 10%

Under compound interest the amount after \(n\) years is \(A=P\left(1+\frac{r}{100}\right)^{n}\). So, for two years, the amount divided by the sum is the square of \(1+\frac{r}{100}\), and its square root gives the rate. Here the ratio turns out to be a perfect square, 121 over 100.

• Amount ÷ sum: \(\displaystyle\left(1+\frac{r}{100}\right)^{2}=\frac{2178}{1800}=\frac{121}{100}\)

• Taking the square root: \(\displaystyle 1+\frac{r}{100}=\frac{11}{10}\)

• So the rate is \(r=10\%\) per annum