Question

when the gleo retro (a trendy commuter car) is brand new, it costs $23,500. each year it loses 15% of its value. what will the car be worth when it is 15 years old?

Explanation:

Step1: Define depreciation formula

This is exponential depreciation. The formula for the value \(V\) after \(t\) years is:
$$V = P(1 - r)^t$$
where \(P\) is initial value, \(r\) is annual depreciation rate, \(t\) is time in years.

Step2: Identify given values

\(P = 23500\), \(r = 0.15\), \(t = 15\)

Step3: Substitute values into formula

$$V = 23500(1 - 0.15)^{15}$$

Step4: Calculate remaining value factor

First compute \(0.85^{15} \approx 0.08735\)

Step5: Compute final value

$$V = 23500 \times 0.08735 \approx 2052.73$$

Answer:

$\approx \$2052.73$