Question

The value of a machine worth $Rs.500000$ is depreciating at the rate of $10\%$ every year. In how many years will its value be reduced to $Rs.364500$

Answer 1

Given: Present Value of machine, $P=Rs.500000$

Rate of depreciation, $R=10\%$ per year

The depreciated value of the machine, $A=Rs.364500$

Time, $T=?$

Depreciated value of the machine is given by

$A=P(1-\frac{R}{100}{)}^T$

$\Rightarrow 364500=500000(1-\frac{10}{100}{)}^T$

$\Rightarrow \frac{364500}{500000}=(1-\frac{1}{10}{)}^T$

$\Rightarrow \frac{729}{1000}=(\frac{9}{10}{)}^T$

$\Rightarrow (\frac{9}{10}{)}^3=(\frac{9}{10}{)}^T$

On comparing, we get

$\Rightarrow T=3$ years.