Question

A manufacturer reckons that the value of a machine, which cost him Rs. 15625 will depreciate each year by $20\%$. Find the estimated value at the end of 5 years.

Answer 1

After one year, value of machine

$=[15625-15625\times \frac{20}{100}]$

$=15625-3125=Rs.12500$

After two years, value of machine

$=[12500-12500\times \frac{20}{100}]$

$=12500-2500=Rs.10000$

After three years, value of machine

$=[10000-10000\times \frac{20}{100}]$

$=10000-2000=Rs.8000$

The sequences of values of machine is 12500, 10000, 8000, ... is a G.P.

Here a = 12500 $r=\frac{10000}{12500}=\frac{4}{5}$

$\therefore a_5=a{r}^4=12500\times {\left(\frac{4}{5}\right)}^4$

$=12500\times \frac{256}{625}=Rs.5120$

Thus the value of machine at the end of 5 years = Rs. 5120.