Question

Based on her past experiences, a homeowner estimates that appliances lose 22% of their resale value each year. If her estimate is accurate, how much will an appliance currently valued at $1,496 be worth in 10 years?
If necessary, round your answer to the nearest cent.

Answer 1

To calculate the value of an appliance after 10 years with a depreciation rate of 22% per year, we can use the formula for exponential decay, which is:

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

where:
- \( V \) is the value after time \( t \)
- \( P \) is the initial value (current value)
- \( r \) is the depreciation rate
- \( t \) is the number of years

Given:
- \( P = 1496 \)
- \( r = 0.22 \)
- \( t = 10 \)

Substituting the values into the formula:

\[
V = 1496 \times (1 - 0.22)^{10}
\]

Calculating \( (1 - 0.22) \):

\[
1 - 0.22 = 0.78
\]

Now substituting back into the equation:

\[
V = 1496 \times (0.78)^{10}
\]

Next, we calculate \( (0.78)^{10} \):

\[
(0.78)^{10} \approx 0.1074
\]

Now, multiply this by the initial value:

\[
V \approx 1496 \times 0.1074 \approx 160.6016
\]

Rounding to the nearest cent, the estimated value of the appliance in 10 years would be:

\[
\boxed{160.60}
\]