On what sum of money will the compound interest for 2 years at 5 per cent per annum amount to ₹ 768.75 ?

Let sum of money be ₹ x.

Given,

n = 2 years

r = 5%

C.I. = ₹ 768.75

A = P + I = ₹ x + ₹ 768.75

By formula,

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

Substituting values we get :

$\Rightarrow x + 768.75 = x \times \Big(1 + \dfrac{5}{100}\Big)^2 \\[1em] \Rightarrow x + 768.75 = x \times \Big(\dfrac{105}{100}\Big)^2 \\[1em] \Rightarrow x + 768.75 = x \times \Big(\dfrac{21}{20}\Big)^2 \\[1em] \Rightarrow x + 768.75 = x \times \dfrac{441}{400} \\[1em] \Rightarrow 400(x + 768.75) = 441x \\[1em] \Rightarrow 400x + 307500 = 441x \\[1em] \Rightarrow 441x - 400x = 307500 \\[1em] \Rightarrow 41x = 307500 \\[1em] \Rightarrow x = \dfrac{307500}{41} \\[1em] \Rightarrow x = ₹7500.$

Hence, sum of money = ₹ 7500.