Question : The price of motorcycles depreciates every year by 8%. If the value of the motorcycle after 2 years will be Rs. 84,640, then what is the present value (in Rs.) of the motorcycle?
Option 1: 90,000
Option 2: 1,02,000
Option 3: 1,10,000
Option 4: 1,00,000
Correct Answer: 1,00,000
Solution :
Let the present value of the motorcycle be $x$.
Value after 2 years $= x × (1-\frac{R}{100})^2$, where $R$ is the rate.
So, $84640 = x × (1-\frac{8}{100})^2$
⇒ $84640 = x × (\frac{23}{25})^2$
⇒ $x =84640 \times \frac{25\times 25}{23 \times 23}$
$\therefore x= 1,00,000$
Present Value = Rs. 1,00,000
Hence, the correct answer is 1,00,000.
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