Question

The value of a flat worth Rs 500000 is depreciating at the rate of $10\%$ per annum. In how many years will its value be reduced to Rs. 364500?

Answer 1

Given,
Present value, P = Rs. 500000, Depreciated value, A = Rs 364500
The rate of depreciation, R $=10\%$ per annum.
Let the depreciation period be of n years.

We have, $A=P[1-\frac{R}{100}{]}^n$
Then, $364500=500000{(1-\frac{10}{100})}^n$
$\Rightarrow \frac{3645}{5000}={\left(\frac{9}{10}\right)}^n$
$\Rightarrow \frac{729}{1000}={\left(\frac{9}{10}\right)}^n\Rightarrow {\left(\frac{9}{10}\right)}^3={\left(\frac{9}{10}\right)}^n\Rightarrow n=3$
Hence, in 3 years the value of the flat be reduced to Rs 364500.