Simple interest on a sum of money for 2 years at 4% is ₹ 450. Find the compound interest on the same sum and at the same rate for 2 years.

Let the sum be ₹ x.

Given,

Simple interest on the sum of money for 2 years at 4% is ₹ 450.

By formula,

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

Substituting values we get :

$\Rightarrow 450 = \dfrac{x \times 4 \times 2}{100} \\[1em] \Rightarrow x = \dfrac{450 \times 100}{8} \\[1em] \Rightarrow x = 225 \times 25 \\[1em] \Rightarrow x = ₹5625.$

By formula,

C.I. = A - P

$= P\Big(1 + \dfrac{r}{100}\Big)^n - P \\[1em] = 5625 \times \Big(1 + \dfrac{4}{100}\Big)^2 - 5625 \\[1em] = 5625 \times \Big(\dfrac{104}{100}\Big)^2 - 5625 \\[1em] = 5625 \times \Big(\dfrac{26}{25}\Big)^2 - 5625 \\[1em] = 5625 \times \dfrac{676}{625} - 5625 \\[1em] = 6084 - 5625 \\[1em] = ₹ 459.$

Hence, the compound interest = ₹ 459.