Question

A used car was purchased for $12329 this year. Each year the car's value decreases by 8.5%. What will the car be worth in 10 years? Round your answer to two decimal places.

Answer 1

To find the value of the car after 10 years, we can use the formula for exponential decay, which is given by:

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

where:
- \( V \) is the future value of the car,
- \( P \) is the initial purchase price,
- \( r \) is the annual depreciation rate (as a decimal),
- \( t \) is the number of years.

In this case:
- \( P = 12329 \)
- \( r = 0.085 \) (since 8.5% as a decimal is 0.085)
- \( t = 10 \)

Plugging in the values:

\[
V = 12329 \times (1 - 0.085)^{10}
\]

Calculating \( (1 - 0.085) \):

\[
1 - 0.085 = 0.915
\]

Now, calculate \( 0.915^{10} \):

\[
0.915^{10} \approx 0.42241 \quad (\text{using a calculator})
\]

Now we can calculate \( V \):

\[
V = 12329 \times 0.42241 \approx 5207.54
\]

Thus, the value of the car after 10 years will be approximately:

\[
\boxed{5207.54}
\]