Nikita invests ₹ 6000 for two years at a certain rate of interest compounded annually. At the end of first year it amounts to ₹ 6720. Calculate :

(a) the rate percent (i.e. the rate of growth)

(b) the amount at the end of the second year.

(a) Let rate percent be r%.

Given,

P = ₹ 6000

n = 1 year

A = ₹ 6720

By formula,

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

Substituting values we get :

$\Rightarrow 6720 = 6000\Big(1 + \dfrac{r}{100}\Big)^1 \\[1em] \Rightarrow \dfrac{6720}{6000} = 1 + \dfrac{r}{100} \\[1em] \Rightarrow \dfrac{6720}{6000} - 1 = \dfrac{r}{100} \\[1em] \Rightarrow \dfrac{6720 - 6000}{6000} = \dfrac{r}{100} \\[1em] \Rightarrow \dfrac{720}{6000} = \dfrac{r}{100} \\[1em] \Rightarrow r = \dfrac{720 \times 100}{6000} \\[1em] \Rightarrow r = 12\%.$

Hence, rate percent = 12%.

(b) By formula,

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

$A = 6000 \times \Big(1 + \dfrac{12}{100}\Big)^2 \\[1em] = 6000 \times \Big(\dfrac{112}{100}\Big)^2 \\[1em] = 6000 \times \Big(\dfrac{28}{25}\Big)^2 \\[1em] = 6000 \times \dfrac{784}{625} \\[1em] = ₹ 7526.40$

Hence, amount at the end of 2 years = ₹ 7526.40