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? [4 MARKS]

Answer 1

Formula : 1 Mark
Application : 1 Mark
Calculation : 2 Marks

We have,

Present value = Rs. 500000, Depreciated value = Rs 364500

Rate of depreciation $=10\%$ per annum.

Let the depreciation period be of n years. 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.