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A new car is purchased for 25000 dollars. The value of the car depreciates at 8.25% per year. What will the value of the car be, to the nearest cent, after 15 years?

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JeanaShupp

Answer: $6871.18

Step-by-step explanation:

The equation for depreciation is given by :-

[tex]y=A(1-r)^x[/tex], where A is the initial value and r is the rate of depreciation in x years.

Given: The initial value of car = $25,000

The rate of depreciation of car = 8.25%=0.0825

Now, the value of car after 15 years will be given by :-

[tex]y=25,000(1-0.0825)^{15}\\\\\Rightarrow y=25000(0.9175)^{15}\\\\\Rightarrow y=\$6871.17647028\approx \$6871.18[/tex]

Hence, the value of car after 15 years= $6871.18

The value of the car is $6871.18 after 15 years.

Given

A new car is purchased for 25000 dollars.

The value of the car depreciates at 8.25% per year.

What is depreciation?

Depreciation is the decrease in the cost of an asset.

To get the depreciation of a partial year, you need to calculate the depreciation a full year first.

The formula to calculate depreciation is given by;

[tex]\rm V = P (1-r)^t[/tex]

Where V represents the depreciation r is the rate of interest and t is the time.

Substitute all the values in the formula;

[tex]\rm V = P (1-r)^t\\\\ V = 25000 (1-\dfrac{8.25}{100})^{15}\\\\V = 25000(1-0.0825){15}\\\\V = 25000(0.9175)^{15}\\\\V = 25000 \times 0.27\\\\V= 6871.18[/tex]

Hence, the value of the car is $6871.18 after 15 years.

To know more about Depreciation click the link given below.

https://brainly.com/question/13734742

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