Question

question
a new car is purchased for 24500 dollars. the value of the car depreciates at 14.75% per year. what will the value of the car be, to the nearest cent, after 14 years?
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Explanation:

Step1: Define depreciation formula

The formula for exponential depreciation is $A = P(1 - r)^t$, where:

• $P = 24500$ (initial value),
• $r = 0.1475$ (annual depreciation rate),
• $t = 14$ (time in years).

Step2: Calculate remaining value factor

First compute $1 - r$:
$1 - 0.1475 = 0.8525$

Step3: Compute factor raised to time

Calculate $0.8525^{14}$:
$0.8525^{14} \approx 0.103247$

Step4: Find final car value

Multiply initial value by the factor:
$A = 24500 \times 0.103247 \approx 2529.55$

Answer:

2529.55 dollars