# The value of a machine depreciates at the rate of 10% per annum.

Question:

The value of a machine depreciates at the rate of 10% per annum. It was purchased 3 years ago. If its present value is Rs 291600, for how much was it purchased?

Solution:

Let the initial value of the machine, $P$ be Rs $x$. Rate of depreciation, $R=10 \%$

Time, $n=3$ years

The present value of the machine is Rs 291600 .

Then the initial value of the machine is given by Value $=P \times\left(1-\frac{R}{100}\right)^{n}$

$=$ Rs. $x \times\left(1-\frac{10}{100}\right)^{3}$

$=$ Rs. $x \times\left(\frac{100-10}{100}\right)^{3}$

$=$ Rs. $x \times\left(\frac{90}{100}\right)^{3}$

$=$ Rs. $x \times\left(\frac{9}{10}\right)^{3}$

$\therefore$ Present value of the machine $=$ Rs 291600

Now, Rs $291600=$ Rs $x \times\left(\frac{9}{10}\right) \times\left(\frac{9}{10}\right) \times\left(\frac{9}{10}\right)$

$\Rightarrow x=$ Rs $\frac{291600 \times 10 \times 10 \times 10}{9 \times 9 \times 9}$

$\Rightarrow x=$ Rs $\frac{291600000}{729}$

$\Rightarrow x=$ Rs 400000

$\therefore$ The initial value of the machine is Rs 400000 .