Question

Sharon purchased a used car for $24,600. The car depreciates exponentially by 8% per
much will the car be worth after 5 years? Round your answer to the nearest penny.

Answer 1

Answer:

The value of car after 5 years of exponentially depreciation is $16,213.36  

Step-by-step explanation:

The initial amount of the car = i = $24,600

The depreciates rate of interest applied = r = 8%

Let The value of car after n years = A  

The number of years = n = 5 years

Now,According to question

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

Or, The value of car after 5 years = i × $(1-\dfrac{\textrm r}{100})^{\textrm n}$

Or, $A = $24,600 × $(1-\dfrac{\textrm 8}{100})^{\textrm 5}$

Or, $A = $24,600 × $(0.92)^{5}$

Or, $A = $24,600 × 0.65908

Or, $A = $16,213.36

So, The value of car after 5 years = A = $16,213.36

Hence , The value of car after 5 years of exponentially depreciation is $16,213.36  . Answer