After deciding to get a new car, you can either lease the car or purchase it wit

Question

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?

Explanation / Answer

Rate per month =7%/12
Number of Period = 4* 12 = 48
PV Cost of Leasing = 103 + 503* ( 1-(1+r)-n)/r = 103 + 503 *(1 -(1+7%/12)-48/7%/12 = 20,902.38

PV Cost of Buying The Car = 37000 - 25000/(1+7%)4 = 17927.62

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