question 12 of 20\nthe original purchase price of a car is $12,000. each year, its value depreciates (loses…

question 12 of 20\nthe original purchase price of a car is $12,000. each year, its value depreciates (loses value) by 5%. three years after its purchase, what is the value of the car?\na. $1.50\nb. $10,830\nc. $10,288.50\nd. $13,891.50

question 12 of 20\nthe original purchase price of a car is $12,000. each year, its value depreciates (loses value) by 5%. three years after its purchase, what is the value of the car?\na. $1.50\nb. $10,830\nc. $10,288.50\nd. $13,891.50

Answer

Explanation:

Step1: Identify the depreciation formula

The formula for compound - depreciation is $A = P(1 - r)^t$, where $P$ is the initial value, $r$ is the rate of depreciation as a decimal, and $t$ is the number of years. Here, $P=$12000$, $r = 0.05$ (since $5%=0.05$), and $t = 3$.

Step2: Substitute the values into the formula

$A=12000\times(1 - 0.05)^3$. First, calculate $1-0.05 = 0.95$. Then, $(0.95)^3=0.95\times0.95\times0.95 = 0.857375$. Next, $A = 12000\times0.857375$. $A=10288.5$.

Answer:

C. $$10,288.50$