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?

Answer #1

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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