Question

Based on her past experiences, a homeowner estimates that appliances lose 27% of their resale value each year. If her estimate is accurate, how much will an appliance currently valued at $1,128 be worth in 10 years?
If necessary, round your answer to the nearest cent.

Answer 1

To calculate the future value of an appliance that loses 27% of its value each year, we can use the formula for exponential decay, which is:

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

where:
- \( V \) is the future value of the appliance,
- \( P \) is the current value of the appliance,
- \( r \) is the rate of value loss, and
- \( t \) is the number of years.

In this case:

- \( P = 1128 \)
- \( r = 0.27 \)
- \( t = 10 \)

Now, substituting the values into the formula:

\[
V = 1128(1 - 0.27)^{10}
\]
\[
V = 1128(0.73)^{10}
\]

Now we calculate \( (0.73)^{10} \):

\[
(0.73)^{10} \approx 0.05764801
\]

Now we substitute this back into the formula:

\[
V \approx 1128 \times 0.05764801 \approx 65.03
\]

Therefore, the appliance will be worth approximately **$65.03** in 10 years.