At what rate per cent per annum compound interest will ₹ 6,250 amount to ₹ 7,290 in 2 years?

Given,

P = ₹ 6,250

A = ₹ 7,290

n = 2 years

Let rate of interest be r%.

By formula,

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

Substituting values we get :

$\Rightarrow 7290 = 6250 \times \Big(1 + \dfrac{r}{100}\Big)^2 \\[1em] \Rightarrow \dfrac{7290}{6250} = \Big(1 + \dfrac{r}{100}\Big)^2 \\[1em] \Rightarrow \dfrac{729}{625} = \Big(1 + \dfrac{r}{100}\Big)^2 \\[1em] \Rightarrow \Big(\dfrac{27}{25}\Big)^2 = \Big(1 + \dfrac{r}{100}\Big)^2 \\[1em] \Rightarrow \dfrac{27}{25} = 1 + \dfrac{r}{100} \\[1em] \Rightarrow \dfrac{27}{25} - 1 = \dfrac{r}{100} \\[1em] \Rightarrow \dfrac{27 - 25}{25} = \dfrac{r}{100} \\[1em] \Rightarrow \dfrac{2}{25} = \dfrac{r}{100} \\[1em] \Rightarrow r = \dfrac{200}{25} = 8\%.$

Hence, rate of interest = 8% p.a.