Question

A car is purchased for $25,000. After each year, the resale value decreases by 30%. What will the resale value be after 5 years?
Use the calculator provided and round your answer to the nearest dollar.

Answer 1

To find the resale value of the car after 5 years, we can use the formula for depreciation based on a percentage decrease. The formula for the resale value after \( n \) years can be expressed as:

\[
V = P \times (1 - r)^n
\]

where:
- \( V \) is the resale value after \( n \) years,
- \( P \) is the initial purchase price,
- \( r \) is the rate of depreciation,
- \( n \) is the number of years.

In this case:
- \( P = 25000 \) (initial purchase price),
- \( r = 0.30 \) (30% depreciation per year),
- \( n = 5 \) (number of years).

Now, plugging in the values:

\[
V = 25000 \times (1 - 0.30)^5
\]

Calculating \( (1 - 0.30) \):

\[
1 - 0.30 = 0.70
\]

Now, calculate \( 0.70^5 \):

\[
0.70^5 = 0.16807
\]

Now, calculate the resale value:

\[
V = 25000 \times 0.16807 \approx 4201.75
\]

Rounding to the nearest dollar, the resale value after 5 years will be:

\[
\boxed{4202}
\]