At what rate per cent will a sum of ₹ 4000 yield ₹ 1324 as compound interest in 3 years ?

Let rate of interest be r%.

Given,

P = ₹ 4000

C.I. = ₹ 1324

A = P + C.I. = ₹ 4000 + ₹ 1324 = ₹ 5324

n = 3 years

By formula,

A = $P\Big(1 + \dfrac{r}{100}\Big)^n$

Substituting values we get :

$\Rightarrow 5324 = 4000 \times \Big(1 + \dfrac{r}{100}\Big)^3 \\[1em] \Rightarrow \dfrac{5324}{4000} = \Big(1 + \dfrac{r}{100}\Big)^3 \\[1em] \Rightarrow \Big(1 + \dfrac{r}{100}\Big)^3 = \dfrac{1331}{1000} \\[1em] \Rightarrow \Big(1 + \dfrac{r}{100}\Big)^3 = \Big(\dfrac{11}{10}\Big)^3 \\[1em] \Rightarrow 1 + \dfrac{r}{100} = \dfrac{11}{10} \\[1em] \Rightarrow \dfrac{r}{100} = \dfrac{11}{10} - 1 \\[1em] \Rightarrow \dfrac{r}{100} = \dfrac{11 - 10}{10} \\[1em] \Rightarrow r = \dfrac{1}{10} \times 100 \\[1em] \Rightarrow r = 10\%.$

Hence, rate of interest = 10%.