Question

A new car is purchased for 18000 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 14 years?

Answer 1

Answer:

The value of car after 14 years is  $ 2,363.04

Step-by-step explanation:

Given as :

The price of new car = N = $ 18,000

The rate of depreciation of the value of the car = R = 13.5 % per year

Let The value of car after 14 years = $ x

The time period = 14 years

Now, According to question

The value of car after n years = initial value of car × $(1-\dfrac{\textrm rate}{100})^{\textrm Time}$

or, $ x = N × $(1-\dfrac{\textrm R}{100})^{\textrm n}$

or, $ x = $ 18,000 × $(1-\dfrac{\textrm 13.5}{100})^{\textrm 14}$

Or, $ x = $ 18,000 × $(0.865)^{14}$

∴  x = $ 18,000 × 0.13128

I.e x = $ 2,363.04

So, The value of car after 14 years =  x = $ 2,363.04

Hence The value of car after 14 years is  $ 2,363.04  Answer