A sum of money invested at compound interest amounts to Rs. 4624 in 2 years and to Rs. 4913 in 3 years. The sum of money is-

Explanation

Let, the principle is Rs. P and rate is R%. Formula - $A = P \left(1 + \frac{x}{100}\right)^x$ According to question, $$P\left(1 + \frac{R}{100}\right)^2 = 4624............(i)$$ $$P\left(1 + \frac{R}{100}\right)^3 = 4913............(ii)$$ On dividing eqⁿ (ii) by eqⁿ (i) $$1 + \frac{R}{100} = \frac{4913}{4624}$$ $$\frac{R}{100} = \frac{4913}{4624} - 1 = \frac{4913 - 4624}{4624}$$ $$R = \frac{289 \times 100}{4624} = \frac{25}{4} \%$$ Putting the value of R in eqⁿ (i) $$P\left(1 + \frac{\frac{25}{4}}{100}\right)^2 = 4624$$ $$P \times \frac{425}{400} \times \frac{425}{400} = 4624$$ $$P = \frac{4624 \times 400 \times 400}{425 \times 425} \Rightarrow 4096$$