Question

A new car is purchased for 19000 dollars. The value of the car depreciates at 11.25% per year. What will the value of the car be, to the nearest cent, after 14 years?

Answer 1

To determine the value of the car after 14 years of depreciation at a rate of 11.25% 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 purchase price of the car,
- \( r \) is the depreciation rate,
- \( t \) is the number of years.

Given:
- \( P = 19000 \)
- \( r = 0.1125 \) (11.25% in decimal)
- \( t = 14 \)

Now we substitute these values into the formula:

\[
V = 19000(1 - 0.1125)^{14}
\]

First, calculate \( 1 - 0.1125 \):

\[
1 - 0.1125 = 0.8875
\]

Now, raise \( 0.8875 \) to the power of \( 14 \):

\[
0.8875^{14} \approx 0.174509
\]

Now we can calculate \( V \):

\[
V \approx 19000 \times 0.174509 \approx 3315.68
\]

Thus, the value of the car after 14 years, rounded to the nearest cent, is approximately **$3315.68**.