Question

Question 8A vehicle purchased for $22400 depreciates at a constant rate of 6% per year. Determine theapproximate value of the vehicle 15 years after purchase.Round to the nearest whole number.

Answer 1

The value of the vehicle after 15 years is $8,855

SOLUTION

Problem Statement

The question tells us a vehicle purchased at $22,400 depreciates at a constant rate of 6% per year and we are required to find the approximate value of the vehicle 15 years after the date of purchase. We are required to round our answer to the nearest whole number.

Method

To find the value of the vehicle after 15 years of depreciating, we need to apply the formula given below:

`\begin{gathered} P=P_0(1+r)^t \\ \text{where,} \\ P_0=\text{ Purchase price of the vehicle} \\ r=\text{The depreciation rate per year} \\ t=\text{The number of years elapsed} \\ \\ (\text{Note: Rate (r) is negative since the vehicle depreciates)} \end{gathered}`

Implementation

`\begin{gathered} P=P_0(1+r)^t \\ P_0=22,400 \\ r=-6\text{ \% }=-(6)/(100)=-0.06 \\ t=15 \\ \\ \therefore P=22,400(1-0.06)^(15) \\ P=22,400(0.94)^(15) \\ P=8,854.5363\approx8,855\text{ (To the nearest whole number)} \end{gathered}`

Final Answer

The value of the vehicle after 15 years is $8,855