The value of a machine depreciates at the rate of $10\%$ per annum. It was purchased 3 years ago. It its present value is Rs. 43740, find its purchased price.

Let the purchase price of machine = Rs. P
Rate of depreciation $=10\%$ p.a.
Period (n) = 3 years.
$\therefore$ and present value = Rs. 43740
$\therefore A=P{(1-\frac{R}{100})}^n$
$\Rightarrow Rs.43740=P{(1-\frac{10}{100})}^3$
$\Rightarrow Rs.43740=P{\left(\frac{9}{10}\right)}^3$
$\therefore P=Rs.43740{\left(\frac{10}{9}\right)}^3$
$=Rs.43740\times \frac{10}{9}\times \frac{10}{9}\times \frac{10}{9}=Rs.60000$
$\therefore$ Value of machine 3 years ago = Rs. 60000.