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A new car is purchased for 16500 dollars. The value of the car depreciates at 5.75% per year. What will the value of the car be, to the nearest cent, after 5 years?

Respuesta :

Aliwohaish12
A=16500(1-0.0575)^5
A=16,500×(1−0.0575)^(5)
A=12,271.30

The value of the car after 5 years is $12271.05

The present value of the car, PV = $16500

The rate of depreciation, r = 5.75%

r  =  5.75/100

r  =  0.0575

Since the car depreciates annually for 5 years:

Number of times of depreciation n = 5

The formula for the Future value of a depreciating asset is given as:

[tex]FV = PV(1-r)^n[/tex]

Substitute PV = 16500, r = 0.0575, and n = 5 into the formula above:

[tex]FV=16500(1-0.0575)^5\\\\FV=16500(0.9425)^5\\\\FV=16500(0.7437)\\\\FV=12271.05[/tex]

The value of the car after 5 years is $12271.05

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