On what sum of money will the compound interest for 2 years at 8% per annum be ₹ 7,488?

Let sum of money be ₹ x.

Given,

P = ₹ x

n = 2 years

r = 8%

C.I. = ₹ 7,488

A = P + I = ₹ x + ₹ 7,488

By formula,

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

Substituting values we get :

$\Rightarrow x + 7488 = x \times \Big(1 + \dfrac{8}{100}\Big)^2 \\[1em] \Rightarrow x + 7488 = x \times \Big(\dfrac{108}{100}\Big)^2 \\[1em] \Rightarrow x + 7488 = x \times \Big(\dfrac{27}{25}\Big)^2 \\[1em] \Rightarrow x + 7488 = x \times \dfrac{729}{625} \\[1em] \Rightarrow 625(x + 7488) = 729x \\[1em] \Rightarrow 625x + 4680000 = 729x \\[1em] \Rightarrow 729x - 625x = 4680000 \\[1em] \Rightarrow 104x = 4680000 \\[1em] \Rightarrow x = \dfrac{4680000}{104} \\[1em] \Rightarrow x = ₹ 45,000.$

Hence, sum of money = ₹ 45,000.