Question

The difference between simple and compunded interests compounded annually on a certain sum of money for 2 years at 4% per annum is Re. 1. The sum is.........

with solution please

Answer 1

$\textbf{SOLUTION:}$

Amount after 2 years on Rs. x at 4℅ per annum when interest is compounded annually

$= x(1 + \frac{4}{100}) ^{2} = x \frac{104}{100} ^{2} \\ \\ compound \: interest \: = x (\frac{104}{100}^{2} )- x \\ \\ = x \binom{104}{100}^{2} - 1 = x \binom{26}{25}^{2}- 1 = \binom{676}{625}- 1 = x \binom{57}{625} = \frac{51x}{625} \\ \\ simple \: initerest \: = \frac{prt}{100} = \frac{x \times 4 \times 2}{100} = \frac{2x}{25} \\ \\ given \: that \: difference \: between \: compound \: interest \: and \: simple \\ interest \: is \: rs.1 \\ \\ \frac{51x}{625} - \frac{2x}{25} = 1 \\ \\ \frac{51x - 50x}{625} = 1 \\ \\ x = 625$