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You want to acquire a new car, but you're not sure whether you should lease it or buy it. You can buy your chosen model for $50,000. You expect it to be worth $20,000 after you use it for three years. Alternatively, you could lease it for $650 per month for a three-year term, with the first payment due immediately. The lease company has not told you what interest rate they're using to calculate the monthly payments, but you know you could borrow money at an annual percentage rate (APR) of 8%.
Problem 1: Calculate the present value of the lease payments, assuming monthly compounding at the given APR of 8%.
Problem 2: Calculate the present value of the $20,000 salvage value, again using monthly compounding and the given APR of 8%. Deduct the salvage value from the purchase price to determine the present value of the cost of buying the vehicle.
Problem 3: Calculate the salvage value at which you should be indifferent between leasing and buying.
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