Calculate the sum of money on which the compound interest (payable annually) for 2 years be four times the simple interest on ₹ 4715 for 5 years, both at the rate of 5 percent per annum.

For S.I. :

P = ₹ 4715

R = 5%

T = 5 years

S.I. = $\dfrac{P \times R \times T}{100} = \dfrac{4715 \times 5 \times 5}{100}$ = ₹ 1178.75

Given,

C.I. is four times the S.I.

∴ C.I. = 4 × 1178.75 = ₹ 4715

For C.I. :

Let P = ₹ x, n = 2 years, r = 5%

By formula,

C.I. = A - P

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

Hence, sum of money = ₹ 46000.