Question

You buy a used camper in 2000 for $25,000. Each year the value of the camper depreciates by 1.8%. To the

nearest dollar, what would the value of the camper be in 5 years?
A.$27,332
B.$22,830
C.$1,826.36
D.$22,848

Answer 1

The value of the camper after 5 years, considering a 1.8% annual depreciation rate, is approximately $22,830 when rounded to the nearest dollar.

Step-by-step explanation:

To calculate the value of the camper after 5 years with annual depreciation of 1.8%, we can apply the formula for exponential decay: V = P(1 - r)^t, where V is the future value of the camper, P is the initial purchase price, r is the depreciation rate, and t is the number of years.

In this case, the initial purchase price (P) is $25,000, the depreciation rate (r) is 0.018 (1.8% expressed as a decimal), and the number of years (t) is 5.

Now let's plug these values into the formula:

1. Convert the depreciation rate from a percentage to a decimal by dividing by 100: 1.8% / 100 = 0.018.
2. Subtract the depreciation rate from 1 to get the yearly depreciation multiplier: 1 - 0.018 = 0.982.
3. Raise this multiplier to the power of t, the number of years: 0.982^5.
4. Multiply this result by the original price of the camper: $25,000 * (0.982^5).
5. Calculate the result to find the value of the camper after 5 years.

When you do the math, you get:

V = $25,000 * (0.982^5) ≈ $22,830

Therefore, the value of the camper after 5 years, rounded to the nearest dollar, would be $22,830.