Question

Ryan's motorcycle is now worth $2500. Ithas depreciated 12% each year since itwas purchased. If he bought it four yearsago, what did it cost brand new? Roundto the nearest dollar

Answer 1

Given a principal of P and a depreciation rate of r %,

after n years the new amount A is given by

$A=P(1-r^{})^n$

In this case,

$A=\text{ \ 2500 r = 12\% n = 4years}$

Then, we have

$\begin{gathered} 2500=P(1-0.12^4) \\ \text{ Which implies that } \\ P=\frac{2500}{(1-0.12)^4}=\frac{2500}{0.88^4}=\frac{2500}{0.5997}=\text{ \ 4169} \end{gathered}$

Hence the cost brand new is $4169