A car dealership wants to try out a new leasing arrangment, 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 three years of ownership. For a car in good condition, the arrangement will value the car at 1/3 the original price at the end of three years, and will depreciate the value of the car linearly over the course of the three years. What is the value of a car with initial purchase price P at the end of the second year? Write your answer as an expression in terms of P. Write the exact answer. Do not round.

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07-10-2022
Mathematics

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A car dealership wants to try out a new leasing arrangment, 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 three years of ownership. For a car in good condition, the arrangement will value the car at 1/3 the original price at the end of three years, and will depreciate the value of the car linearly over the course of the three years. What is the value of a car with initial purchase price P at the end of the second year? Write your answer as an expression in terms of P. Write the exact answer. Do not round.

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