Question

A new car is purchased for 17000 dollars. The value of the car depreciates at 13.5% per year. What will the value of the car be, to the nearest cent, after 12 years?

Answer 1

The value of car after 12 years is $ 2982.92

Solution:

Given that,

A new car is purchased for 17000 dollars

The value of the car depreciates at 13.5% per year

To find: Value of car after 12 years

The decreasing function is given as:

$y = a(1-r)^t$

Where,

y is the future value

a is the initial value

r is the decreasing rate in decimal

t is the number of years

From given,

$a = 17000\\\\t = 12\\\\r = 13.5 \% = \frac{13.5}{100} = 0.135$

Substituting the values we get,

$y = 17000(1-0.135)^{12}\\\\y = 17000(0.865)^{12}\\\\y = 17000 \times 0.1754661\\\\y = 2982.9241 \approx 2982.92$

Thus value of car after 12 years is $ 2982.92