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QuestionA car was bought for \$25,000 and is worth \$2800 after 6 years. Find its value at the end of year 3 assuming steady depreciation.

Studdy Solution

STEP 1

Assumptions1. The initial purchase price of the car is \$25,000. The value of the car after6 years is \$28003. The car's value depreciates steadily each year

STEP 2

First, we need to find the total depreciation of the car over the6 years. We can do this by subtracting the value of the car after6 years from the initial purchase price.
Total Depreciation=Initial Purchase Price−Value after 6 yearsTotal\, Depreciation = Initial\, Purchase\, Price - Value\, after\,6\, years

STEP 3

Now, plug in the given values for the initial purchase price and the value after6 years to calculate the total depreciation.
Total Depreciation=$25,000−$2800Total\, Depreciation = \$25,000 - \$2800

STEP 4

Calculate the total depreciation.
Total Depreciation=$25,000−$2800=$22,200Total\, Depreciation = \$25,000 - \$2800 = \$22,200

STEP 5

Now that we have the total depreciation, we can find the annual depreciation by dividing the total depreciation by the number of years ().
Annual Depreciation=Total Depreciation/Number of yearsAnnual\, Depreciation = Total\, Depreciation / Number\, of\, years

STEP 6

Plug in the values for the total depreciation and the number of years to calculate the annual depreciation.
Annual Depreciation=$22,200/6Annual\, Depreciation = \$22,200 /6

STEP 7

Calculate the annual depreciation.
Annual Depreciation=$22,200/6=$3700Annual\, Depreciation = \$22,200 /6 = \$3700

STEP 8

Now that we have the annual depreciation, we can find the value of the car at the end of the third year by subtracting three times the annual depreciation from the initial purchase price.
Value at end of third year=Initial Purchase Price−3timesAnnual DepreciationValue\, at\, end\, of\, third\, year = Initial\, Purchase\, Price -3 \\times Annual\, Depreciation

STEP 9

Plug in the values for the initial purchase price and the annual depreciation to calculate the value at the end of the third year.
Value at end of third year=$25,000−3times$370Value\, at\, end\, of\, third\, year = \$25,000 -3 \\times \$370

STEP 10

Calculate the value of the car at the end of the third year.
Value at end of third year=$25,000−3times$3700=$14,900Value\, at\, end\, of\, third\, year = \$25,000 -3 \\times \$3700 = \$14,900The value of the car at the end of the third year is \$14,900.

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