Question

A new car is purchased for 18000 dollars. the value of the car depriciates at 13.5% per year. what will the value of the car be, to the nearest cent, after 14 years?

Answer 1

The value of the car will be $2,363.19 after 14 years

Explanation:

The rule of depreciating is

`A=p(1-r)^(t)` , where

• A is the new value

• P is the original value

• r is the rate in decimal

• t is the time in years

∵ A new car is purchased for 18000 dollars

∴ P = 18,000

∵ It depreciates at a rate of 13.5% per year

∴ r = 13.5% = 13.5/100 = 0.135

∵ We need to find how much it will be worth after 14 years

∴ t = 14

→ Substitute all of these values in the rule above to find A

∵
`A=18000(1-0.135)^(14)`

→ Use your calculator to find the answer

∴ A = 2,363.186569

→ Round it to the nearest cent (2d.p.)

∴ A = 2,363.19

∴ The value of the car will be $2,363.19 after 14 years.