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Math  /  Algebra

QuestionOriginal cost, $55,000\$ 55,000, life, 10 years, annual rate of value lost, 14%14 \% s=$\mathrm{s}=\$ (Round to the nearest cent.)

Studdy Solution

STEP 1

1. The original cost of the item is $55,000.
2. The life of the item is 10 years.
3. The item loses value at an annual rate of 14%.
4. We need to calculate the salvage value \( s \) after 10 years.
5. The value should be rounded to the nearest cent.

STEP 2

1. Understand the concept of depreciation.
2. Define the formula for depreciation.
3. Calculate the depreciation over 10 years.
4. Calculate the salvage value.
5. Round the result to the nearest cent.

STEP 3

Understand the concept of depreciation.
Depreciation is the reduction in the value of an asset over time. In this problem, the asset loses 14% of its value each year.

STEP 4

Define the formula for depreciation.
The formula for calculating the future value of an asset after depreciation is given by:
Future Value=Original Cost×(1−Depreciation Rate)Number of Years \text{Future Value} = \text{Original Cost} \times (1 - \text{Depreciation Rate})^{\text{Number of Years}}

STEP 5

Calculate the depreciation over 10 years.
Substitute the given values into the formula:
Future Value=55000×(1−0.14)10 \text{Future Value} = 55000 \times (1 - 0.14)^{10}

STEP 6

Calculate the salvage value.
First, calculate (1−0.14)10 (1 - 0.14)^{10} :
(1−0.14)=0.86 (1 - 0.14) = 0.86 0.8610≈0.2631 0.86^{10} \approx 0.2631
Now, calculate the future value:
Future Value=55000×0.2631≈14470.5 \text{Future Value} = 55000 \times 0.2631 \approx 14470.5

STEP 7

Round the result to the nearest cent.
The salvage value, rounded to the nearest cent, is:
14470.50 \boxed{14470.50}

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