Question

A car dealership wants to try out a new leasing arrangement, which will allow a buyer to trade a car back to the dealership for a certain amount of credit at any time throughout the first four years of ownership. For a car in good condition, the arrangement will value the car at the original price at the end of four years, and will depreciate the value of the car linearly over the course of the four years. What is the value of a car with initial purchase price P at the end of the first year? Write your answer as an expression in terms of P. Write the exact answer. Do not round.

Answer 1

So, the value of the car at the end of the first year is (3P/4).

Explanation:

If the value of the car depreciates linearly over the course of four years and it's valued at the original price at the end of four years, you can calculate the annual depreciation.

Let "V" be the value of the car at the end of the first year, and "P" be the initial purchase price.

Over four years, the car depreciates from P to 0, which is a total depreciation of P - 0 = P. Since this depreciation happens over four years, you can calculate the annual depreciation:

Annual Depreciation = Total Depreciation / Number of Years = P / 4

Now, to find the value of the car at the end of the first year, subtract the annual depreciation from the initial purchase price:

V = P - Annual Depreciation

V = P - (P / 4)

Now, combine like terms:

V = (4P/4) - (P/4)

V = (3P/4)

So, the value of the car at the end of the first year is (3P/4).