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A new car is purchased for $18,000 and over time its value depreciates by one halfevery 6 years. What is the value of the car 19 years after it was purchased, to thenearest hundred dollars?

Answer :

We have the following:

We must pass the time from 19 years to periods of 6 years, as follows

[tex]\frac{19}{6}=3.17[/tex]

That is, 19 years are 3.17 periods of 6 years

now, the formula to calculate the value of the car is

[tex]c=A\cdot(1-x)^n[/tex]

Where A is the initial value, x is the depreciation and n is the time in periods of 6 years

Replacing:

[tex]c=18000\cdot(1-0.5)^{3.17}=1999.89[/tex]

Therefore the value of the car would be approximately 1999.9 dollars

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