After deciding to get a new car, you can either lease the car or purchase it with a four-year loan. The car you wish to buy costs $37,000. The dealer has a special leasing arrangement where you pay $103 today and $503 per month for the next four years. If you purchase the car, you will pay it off in monthly payments over the next four years at an APR of 7 percent, compounded monthly. You believe that you will be able to sell the car for $25,000 in four years. What is the cost today of purchasing the car?
If you plan to purchase the car today, then you would have to pay the cost of car upfront = $37,000
However, you would get some amount back when you sell the car after 4 year.
Net price = Cost paid today - PV of the amount received after 4 years
In order to calculate the PV of the amount received after 4 years, we will use the baisc TVM function FV = PV * (1 + r)n
r = 7%/12 = 0.583% (monthly), n = 12 * 4 months = 48 months
PV = 25,000/(1 + 0.583%)48
PV = 25,000/1.3221 = $18,909.97
Net price = 37,000 - 18,909.97 = $18,090.03
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