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 $500\times(1.1)^{10}$