A certain sum of money amounts to ₹ 23400 in 3 years at 10% per annum simple interest. Find the amount of the same sum in 2 years at 10% p.a. compound interest.

Let sum of money be ₹ x.

Given,

It amounts to ₹ 23400 in 3 years at 10% per annum simple interest.

By formula,

$\Rightarrow A = P + S.I. \\[1em] \Rightarrow 23400 = x + \dfrac{x \times 10 \times 3}{100} \\[1em] \Rightarrow 23400 = x + \dfrac{3x}{10} \\[1em] \Rightarrow \dfrac{13x}{10} = 23400 \\[1em] \Rightarrow x = \dfrac{23400 \times 10}{13} \\[1em] \Rightarrow x = ₹ 18000.$

In case of compound interest :

By formula,

$A = P\Big(1 + \dfrac{r}{100}\Big)^n \\[1em] = 18000 \times \Big(1 + \dfrac{10}{100}\Big)^2 \\[1em] = 18000 \times \Big(\dfrac{110}{100}\Big)^2 \\[1em] = 18000 \times \Big(\dfrac{11}{10}\Big)^2 \\[1em] = 18000 \times \Big(\dfrac{121}{100}\Big) \\[1em] = ₹ 21780.$

Hence, amount on same sum in 2 years at 10% p.a. compound interest = ₹ 21780.