Question

A new car is purchased for 20000 dollars. The value of the car depreciates at 12.5% per year. What will the value of the car be, to the nearest cent, after 11 years?

Answer 1

To calculate the value of the car after 11 years, we can use the formula for exponential decay, which is given by:

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

where:
- \( V \) is the value of the car after \( t \) years,
- \( P \) is the initial value of the car (20000 dollars),
- \( r \) is the depreciation rate (12.5% or 0.125),
- \( t \) is the number of years (11 years).

First, let's substitute the values into the equation:

\[
V = 20000 \times (1 - 0.125)^{11}
\]

Calculating \( (1 - 0.125) \):

\[
1 - 0.125 = 0.875
\]

Now raising \( 0.875 \) to the power of \( 11 \):

\[
0.875^{11} \approx 0.293686
\]

Now, substituting back into the equation for \( V \):

\[
V \approx 20000 \times 0.293686
\]

Calculating this gives:

\[
V \approx 5873.72
\]

Thus, the value of the car after 11 years, to the nearest cent, is approximately:

\[
\boxed{5873.72}
\]