On what sum of money will compound interest (payable annually) for 2 years be the same as simple interest on ₹ 9430 for 10 years, both at the rate of 5 percent per annum ?

For S.I. :

P = ₹ 9430

T = 10 years

R = 5%

$S.I. = \dfrac{P \times R \times T}{100} \\[1em] = \dfrac{9430 \times 5 \times 10}{100} \\[1em] = ₹ 4715.$

Since, C.I. = S.I. = ₹ 4715

Let sum on which C.I. = ₹ 4715 for 2 years at 5% be ₹x.

$\Rightarrow C.I. = A - P \\[1em] \Rightarrow 4715 = P\Big(1 + \dfrac{r}{100}\Big)^n - P \\[1em] \Rightarrow 4715 = x \times \Big(1 + \dfrac{5}{100}\Big)^2 - x \\[1em] \Rightarrow 4715 = x \times \Big(\dfrac{105}{100}\Big)^2 - x \\[1em] \Rightarrow 4715 = x \times \Big(\dfrac{21}{20}\Big)^2 - x \\[1em] \Rightarrow 4715 = \dfrac{441x}{400} - x \\[1em] \Rightarrow 4715 = \dfrac{441x - 400x}{400} \\[1em] \Rightarrow 4715 = \dfrac{41x}{400} \\[1em] \Rightarrow x = \dfrac{4715 \times 400}{41} \\[1em] \Rightarrow x = 115 \times 400 \\[1em] \Rightarrow x = ₹ 46000.$

Hence, sum of money = ₹ 46000.