Question

The cost of car, purchased 2 years ago, depreciates at the rate of $20\%$ every year. If its present worth is Rs.315600, find its purchase price.

• A. Rs. 493125
• B. Rs. 493175
• C. Rs. 493525
• D. Rs. 496725

Answer 1

The correct option is

A

Rs. 493125

Here, P = present value = Rs 315600, t = 2 years, r = $20\%$,

Let, $P_0$ = Purchase price

Using $P=P_0{(1-\frac{r}{100})}^n$
$315600=P_0{(1-\frac{20}{100})}^{2}315600=P_0{\left(\frac{80}{100}\right)}^2=P_0\frac{(4\times 4)}{(5\times 5)}=P_0\left(\frac{16}{25}\right)P_0=315600\times \frac{25}{16}=Rs.493125$

So, the purchase price of the car is Rs. 493125