Question

Kevin’s brand new $50,000 car will depreciate in value by 16% each year. How much will it be worth after 6 years?

Answer 1

To find the value of Kevin's car after 6 years, we need to apply the depreciation rate of 16% each year to the initial value of $50,000. The depreciation formula can be expressed as follows:

\[
\text{Value after } n \text{ years} = \text{Initial Value} \times (1 - \text{Depreciation Rate})^n
\]

Plugging in the values:

- Initial Value = $50,000
- Depreciation Rate = 16% = 0.16
- n = 6 years

We have:

\[
\text{Value after 6 years} = 50000 \times (1 - 0.16)^6
\]

Calculating \(1 - 0.16\):

\[
1 - 0.16 = 0.84
\]

Now, calculate \(0.84^6\):

\[
0.84^6 \approx 0.418211
\]

Now, multiply by the initial value:

\[
\text{Value after 6 years} \approx 50000 \times 0.418211
\]

Calculating this product gives:

\[
\text{Value after 6 years} \approx 20910.55
\]

Thus, the estimated value of the car after 6 years will be approximately **$20,910.55**.