The simple interest on a certain sum of money at 10% per annum is ₹ 6000 in 2 years. Find :

(i) the sum

(ii) the amount due at the end of 3 years and at the same rate of interest compounded annually.

(iii) the compound interest earned in 3 years.

(i) Let the sum be ₹ x.

Given, S.I. = ₹ 6000 in 2 years at 10% rate of interest.

By formula,

S.I. = $\dfrac{P \times R \times T}{100}$

Substituting values we get :

$\Rightarrow 6000 = \dfrac{x \times 10 \times 2}{100} \\[1em] \Rightarrow x = \dfrac{6000 \times 100}{10 \times 2} \\[1em] \Rightarrow x = 30000.$

Hence, sum = ₹ 30000.

(ii) By formula,

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

Substituting values we get :

$A = 30000 \times \Big(1 + \dfrac{10}{100}\Big)^3 \\[1em] = 30000 \times \Big(\dfrac{110}{100}\Big)^3 \\[1em] = 30000 \times \Big(\dfrac{11}{10}\Big)^3 \\[1em] = 30000 \times \dfrac{1331}{1000} \\[1em] = 39930.$

Hence, amount due at the end of 3 years = ₹ 39930.

(iii) By formula,

C.I. = A - P = ₹ 39930 - ₹ 30000 = ₹ 9930.

Hence, compound interest earned in 3 years = ₹ 9930.