a national study found that a cars value decreases by 15 percent annually. if the car was purchased for…

a national study found that a cars value decreases by 15 percent annually. if the car was purchased for $66,000, how much will the car be worth in 10 years? a) $13,792.14 b) $11,768.35 c) $12,993.71 d) $18,429.50

a national study found that a cars value decreases by 15 percent annually. if the car was purchased for $66,000, how much will the car be worth in 10 years? a) $13,792.14 b) $11,768.35 c) $12,993.71 d) $18,429.50

Answer

Explanation:

Step1: Identify the formula for depreciation

The formula for exponential - decay (depreciation) is $A = P(1 - r)^t$, where $A$ is the final amount, $P$ is the initial amount, $r$ is the rate of decay as a decimal, and $t$ is the number of time - periods.

Step2: Convert the percentage to a decimal

The rate of depreciation $r = 15%=0.15$, the initial value of the car $P = 66000$, and the number of years $t = 10$.

Step3: Substitute the values into the formula

$A=66000\times(1 - 0.15)^{10}=66000\times0.85^{10}$.

Step4: Calculate $0.85^{10}$

$0.85^{10}\approx0.1968744$.

Step5: Calculate the final value of the car

$A = 66000\times0.1968744\approx12993.71$.

Answer:

C. $12,993.71$