Question

the original value of a car is $22,000, and it depreciates (loses value) by 15% each year. what is the value of the car after three years?

a. $56,595
b. $15,895
c. $13,510.75
d. $74.25

Explanation:

Step1: Identify the formula for depreciation

The formula for exponential depreciation is $V = P(1 - r)^t$, where $V$ is the final value, $P$ is the principal (original value), $r$ is the rate of depreciation (in decimal), and $t$ is the time in years.
Here, $P = 22000$, $r = 0.15$ (since 15% = 0.15), and $t = 3$.

Step2: Substitute the values into the formula

First, calculate $(1 - r)$: $1 - 0.15 = 0.85$.
Then, raise this to the power of $t$: $0.85^3$. Let's calculate $0.85^3$: $0.85\times0.85 = 0.7225$; $0.7225\times0.85 = 0.614125$.
Now, multiply by $P$: $V = 22000\times0.614125$.

Step3: Calculate the final value

$22000\times0.614125 = 13510.75$.

Answer:

C. $13,510.75$