Question

A car was bought in February 1, 2015 for $25,000, and its value depreciates by 1.5% every single month. The value of the car m months since February 1, 2015 is given by the formula V(m)=25,000(r)m. Find the value of the car on June 1, 2017. Round your answer to the nearest cent.

Answer 1

Answer:

$16,373.99

Explanation:

The value of the car m months since February 1, 2015, is given by the formula:

$V\left(m\right)=25,000\left(r\right)^m$

First, find the value of r.

Since the car's value depreciates by 1.5% every single month, then:

$r=1-1.5\%=1-0.015=0.985$

Next, determine the number of months between February 1, 2015, and June 1, 2017.

• The number of months, m = 10 + 12 + 6 = 28 months

Substitute these values into V(m):

$\begin{gathered} V(28)=25000(0.985)^{28} \\ =\ 16373.99 \end{gathered}$

The value of the car on June 1, 2017, is $16,373.99 (correct to the nearest cent).