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?

Answer 1

To calculate the value of the car after 10 years, we can use the formula for exponential decay:

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

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

Given:
- \( P = 12329 \)
- \( r = 0.085 \)
- \( t = 10 \)

Substituting the values into the formula:

\[
V = 12329(1 - 0.085)^{10}
\]
\[
V = 12329(0.915)^{10}
\]

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

\[
(0.915)^{10} \approx 0.4138
\]

Now, we can substitute this back into the equation:

\[
V \approx 12329 \times 0.4138 \approx 5095.43
\]

Therefore, the value of the car after 10 years will be approximately **$5095.43**.