Question

how much is a sailboat worth 45,000 worth after 4 years of a 12% depreciation after each year in value to the nearest dollar

Answer 1

To calculate the value of a sailboat after 4 years of 12% annual depreciation, you can use the formula for depreciation:

\[
\text{Future Value} = \text{Current Value} \times (1 - \text{Depreciation Rate})^n
\]

Where:
- Current Value is the initial value of the sailboat ($45,000)
- Depreciation Rate is 12% or 0.12
- \( n \) is the number of years (4)

Now let's substitute the values into the formula:

\[
\text{Future Value} = 45000 \times (1 - 0.12)^4
\]

Calculating \( (1 - 0.12) \):

\[
1 - 0.12 = 0.88
\]

Now, raise \( 0.88 \) to the power of 4:

\[
0.88^4 \approx 0.59969536
\]

Now multiply by the initial value:

\[
\text{Future Value} \approx 45000 \times 0.59969536 \approx 26986.78
\]

Rounding to the nearest dollar, the value of the sailboat after 4 years is approximately:

\[
\boxed{26987}
\]