The ratio of compound interest to simple interest on a certain sum for a period of 2 years is 26 : 25. Find the rate of interest per annum.

Question

Prepp Team · Accepted Answer

For a sum $P$ at rate $r\%$ per annum over 2 years:Simple interest: $SI = \dfrac{2Pr}{100}$.Compound interest: $CI = P\left[\left(1+\dfrac{r}{100}\right)^2 - 1\right] = P\left[\dfrac{2r}{100} + \dfrac{r^2}{10000}\right]$.So $\dfrac{CI}{SI} = \dfrac{\frac{2r}{100}+\frac{r^2}{10000}}{\frac{2r}{100}} = 1 + \dfrac{r}{200}$.Given $\dfrac{CI}{SI} = \dfrac{26}{25}$, so $1+\dfrac{r}{200} = \dfrac{26}{25} \Rightarrow \dfrac{r}{200} = \dfrac{1}{25}$.Solving, $r = \dfrac{200}{25} = 8$. The rate of interest is 8% per annum.

Prepp Team · Answer

5%

Prepp Team · Answer

6%

Prepp Team · Answer

4%

UPTET 2026 (Paper 1 & 2) Mock Test Series

Start Your Preparation with Prepp Mobile App