Question

a new car is sold for its sticker value of $19,400. three years later the customer returns to the car dealership to trade the car in. she is told that her car now has a value of $12,105. what is the rate of decline in the value of the car? In your final answer, include all of your calculations.

Answer 1

The rate of decline is
`r=0.1455` or
`r=14.55\%`

Explanation:

we know that

The formula to calculate the depreciated value is equal to

`D=P(1-r)^(t)`

where

D is the depreciated value

P is the original value

r is the rate of depreciation in decimal

t is Number of Time Periods

in this problem we have

`P=\$19,400\\D=\$12,105\\t=3\ years`

substitute in the formula above and solve for r

`\$12,105=\$19,400(1-r)^(3)`

Simplify

`(12,105/19,400)=(1-r)^(3)`

`(1-r)=\sqrt[3]{(12,105/19,400)}`

`r=1-\sqrt[3]{(12,105/19,400)}`

`r=0.1455`

Convert to percentage

`r=14.55\%`