At what rate per cent per annum will ₹ 3,000 amount to ₹ 3,993 in 3 years, the interest being compounded annually?

Given,

P = ₹ 3,000

A = ₹ 3,993

n = 3 years

Let rate of interest be r%.

By formula,

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

Substituting values we get :

$\Rightarrow 3993 = 3000 \times \Big(1 + \dfrac{r}{100}\Big)^3 \\[1em] \Rightarrow \dfrac{3993}{3000} = \Big(1 + \dfrac{r}{100}\Big)^3 \\[1em] \Rightarrow \dfrac{1331}{1000} = \Big(1 + \dfrac{r}{100}\Big)^3 \\[1em] \Rightarrow \Big(\dfrac{11}{10}\Big)^3 = \Big(1 + \dfrac{r}{100}\Big)^3 \\[1em] \Rightarrow \dfrac{11}{10} = 1 + \dfrac{r}{100} \\[1em] \Rightarrow \dfrac{11}{10} - 1 = \dfrac{r}{100} \\[1em] \Rightarrow \dfrac{11 - 10}{10} = \dfrac{r}{100} \\[1em] \Rightarrow \dfrac{1}{10} = \dfrac{r}{100} \\[1em] \Rightarrow r = \dfrac{100}{10} = 10\%.$

Hence, rate of interest = 10% p.a.