Question

Debbie wants to purchase a used car that had a sticker price of $18,500 brand new. The car is currently 4 years old. What is its current value using the rule of thumb that a vehicle loses 15% of its current value each year?
$9,657
$15,725
$11,361
$13,366

Answer 1

To calculate the current value of the car using the rule of thumb that a vehicle loses 15% of its current value each year, we'll apply the formula for depreciation.

The formula for calculating the value \( V \) of the car after \( n \) years is:

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

where:
- \( P \) is the original price of the car,
- \( r \) is the annual depreciation rate (as a decimal),
- \( n \) is the number of years.

In this case:
- \( P = 18500 \) (original price),
- \( r = 0.15 \) (15% depreciation annually),
- \( n = 4 \) (the car is 4 years old).

Plugging in the values:

\[
V = 18500 \times (1 - 0.15)^4
\]
\[
V = 18500 \times (0.85)^4
\]
\[
V = 18500 \times 0.52200625 \quad (\text{calculated from } 0.85^4)
\]
\[
V \approx 18500 \times 0.52200625 \approx 9667.61
\]

Rounding to the nearest dollar:

\[
V \approx 9668
\]

Now comparing it to the provided options, the closest match to $9,668 is:

**$9,657**

Thus, the current value of the car is approximately **$9,657**.