Math / Algebra

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A new car is purchased for 20300 dollars. The value of the car depreciates at $8.75 \%$ per year. What will the value of the car be, to the nearest cent, after 12 years?
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Studdy Solution

STEP 1

1. The initial value of the car is $20,300.
2. The car depreciates at a rate of $8.75\%$ per year.
3. We need to find the value of the car after 12 years.
4. Depreciation is compounded annually.

STEP 2

1. Understand the concept of depreciation.
2. Define the formula for depreciation.
3. Substitute the given values into the formula.
4. Calculate the value of the car after 12 years.

STEP 3

Understand the concept of depreciation.
Depreciation is the reduction in the value of an asset over time. In this case, the car's value decreases by a certain percentage each year.

STEP 4

Define the formula for depreciation.
The formula to calculate the depreciated value of an asset is:
$V = P(1 - r)^t$
where: - $V$ is the value of the car after $t$ years, - $P$ is the initial value of the car, - $r$ is the annual depreciation rate (as a decimal), - $t$ is the time in years.

STEP 5

Substitute the given values into the formula.
Given: - $P = 20300$ - $r = 8.75\% = 0.0875$ - $t = 12$
Substitute these into the formula:
$V = 20300(1 - 0.0875)^{12}$

STEP 6

Calculate the value of the car after 12 years.
First, calculate $1 - 0.0875$ :
$1 - 0.0875 = 0.9125$
Now raise $0.9125$ to the power of 12:
$0.9125^{12} \approx 0.3491$
Multiply this result by the initial value:
$V = 20300 \times 0.3491 \approx 7086.73$
Thus, the value of the car after 12 years, to the nearest cent, is:
$\boxed{7086.73}$

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Studdy Solution

STEP 1

1. The initial value of the car is $20,300.
2. The car depreciates at a rate of \(8.75\%\) per year.
3. We need to find the value of the car after 12 years.
4. Depreciation is compounded annually.

STEP 2

1. Understand the concept of depreciation.
2. Define the formula for depreciation.
3. Substitute the given values into the formula.
4. Calculate the value of the car after 12 years.

STEP 3

Understand the concept of depreciation.
Depreciation is the reduction in the value of an asset over time. In this case, the car's value decreases by a certain percentage each year.

STEP 4

Define the formula for depreciation.
The formula to calculate the depreciated value of an asset is:
$V = P(1 - r)^t$
where: - $V$ is the value of the car after $t$ years, - $P$ is the initial value of the car, - $r$ is the annual depreciation rate (as a decimal), - $t$ is the time in years.

STEP 5

Substitute the given values into the formula.
Given: - $P = 20300$ - $r = 8.75\% = 0.0875$ - $t = 12$
Substitute these into the formula:
$V = 20300(1 - 0.0875)^{12}$

STEP 6

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Studdy Solution

STEP 1

1. The initial value of the car is $20,300.2. The car depreciates at a rate of \(8.75\%\) per year.3. We need to find the value of the car after 12 years.4. Depreciation is compounded annually.

STEP 2

1. Understand the concept of depreciation.2. Define the formula for depreciation.3. Substitute the given values into the formula.4. Calculate the value of the car after 12 years.

STEP 3

Understand the concept of depreciation.Depreciation is the reduction in the value of an asset over time. In this case, the car's value decreases by a certain percentage each year.

STEP 4

STEP 5

Substitute the given values into the formula.Given: - P=20300 P = 20300 P=20300 - r=8.75%=0.0875 r = 8.75\% = 0.0875 r=8.75%=0.0875 - t=12 t = 12 t=12Substitute these into the formula:V=20300(1−0.0875)12 V = 20300(1 - 0.0875)^{12} V=20300(1−0.0875)12

STEP 6

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Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

1. The initial value of the car is $20,300.
2. The car depreciates at a rate of \(8.75\%\) per year.
3. We need to find the value of the car after 12 years.
4. Depreciation is compounded annually.

1. Understand the concept of depreciation.
2. Define the formula for depreciation.
3. Substitute the given values into the formula.
4. Calculate the value of the car after 12 years.

Understand the concept of depreciation.
Depreciation is the reduction in the value of an asset over time. In this case, the car's value decreases by a certain percentage each year.

Substitute the given values into the formula.
Given: - $P = 20300$ - $r = 8.75\% = 0.0875$ - $t = 12$
Substitute these into the formula:
$V = 20300(1 - 0.0875)^{12}$