A certain sum becomes \(\frac{36}{25}\) of itself after 2 years on compound interest. Find the rate of interest per annum.
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 20%
At compound interest a sum is multiplied by \(\left(1+\frac{r}{100}\right)\) every year, so in 2 years it is multiplied by the square of that factor.
Growth over the 2 years: \(\left(1+\frac{r}{100}\right)^2=\frac{36}{25}\)
Growth in one year (the positive square root): \(1+\frac{r}{100}=\frac{6}{5}\)
\(\frac{r}{100}=\frac{1}{5}\), so \(r=20\%\)