Question

Chase buys a car for $31,556. His car immediately starts depreciating, losing 10% of its value every year. How much will the car be worth in 10 years?
If necessary, round your answer to the nearest cent.

Answer 1

To find the value of the car after 10 years of depreciation at a rate of 10% per year, 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 ($31,556),
- \( r \) is the rate of depreciation (10% or 0.10),
- \( t \) is the number of years (10 years).

Substituting the values into the formula:

\[
V = 31,556 \times (1 - 0.10)^{10}
\]
\[
V = 31,556 \times (0.90)^{10}
\]

Now, we calculate \( (0.90)^{10} \):

\[
(0.90)^{10} \approx 0.3487
\]

Now we can calculate \( V \):

\[
V = 31,556 \times 0.3487 \approx 10,981.83
\]

Therefore, the value of the car after 10 years will be approximately **$10,981.83**.