Question
how much is a sailboat worth 45,000 worth after 4 years of a 12% depreciation in value to the nearest dollar
Answers
GPT-4o mini
To calculate the depreciation of the sailboat over 4 years with a 12% annual depreciation rate, we can use the formula for depreciation:
\[
V = P(1 - r)^t
\]
where:
- \( V \) is the future value of the sailboat,
- \( P \) is the initial purchase price (in this case, $45,000),
- \( r \) is the annual depreciation rate (12% or 0.12),
- \( t \) is the number of years (4).
Plugging in the values:
\[
V = 45000 \times (1 - 0.12)^4
\]
\[
V = 45000 \times (0.88)^4
\]
\[
V = 45000 \times 0.59969536 \, (\text{approximately})
\]
\[
V \approx 45000 \times 0.5997
\]
\[
V \approx 26988.15
\]
Rounding to the nearest dollar, the sailboat is worth approximately **$26,988** after 4 years.
\[
V = P(1 - r)^t
\]
where:
- \( V \) is the future value of the sailboat,
- \( P \) is the initial purchase price (in this case, $45,000),
- \( r \) is the annual depreciation rate (12% or 0.12),
- \( t \) is the number of years (4).
Plugging in the values:
\[
V = 45000 \times (1 - 0.12)^4
\]
\[
V = 45000 \times (0.88)^4
\]
\[
V = 45000 \times 0.59969536 \, (\text{approximately})
\]
\[
V \approx 45000 \times 0.5997
\]
\[
V \approx 26988.15
\]
Rounding to the nearest dollar, the sailboat is worth approximately **$26,988** after 4 years.