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=(2500)/((1-0.12)^4)=(2500)/(0.88^4)=(2500)/(0.5997)=\text{ \$4169} \end{gathered}`

Hence the cost brand new is $4169