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# What will Rs. 500 amounts to in $10$ years after its deposit in a bank which pays annual interest of $10%$ compounded annually?

Given: the initial deposit $=Rs.500$
The interest rate $=10$%
After one year the amount $=500+\large\frac{10}{100}$$\times 500 \qquad\qquad\:=500\big(1+\large\frac{1}{10}$$\big)=500\times 1.1$
After two years the amount is $500\times 1.1+\large\frac{10}{100}$$\times (500\times 1.1)$
$\qquad\qquad\:=500\times1.1\big(1+\large\frac{10}{100}\big)$
$\qquad\qquad\:=500\times1.1\times 1.1$
$\qquad\qquad\:=500\times(1.1)^2$
$\therefore$ The amount forms the series $500 (1.1),\:\:500 (1.1)^2,\:\:500(1.1)^3.........$
in the subsequent years which forms a G.P.
$\therefore$ The amount after 10 years is $10^{th}$ term of this series
which is $500\times(1.1)^{10}$