Problem 4-60 Calculating Annuity Values After deciding to get a new car, you can

Question

Problem 4-60 Calculating Annuity Values

After deciding to get a new car, you can either lease the car or purchase it with a two-year loan. The car you wish to buy costs $30,500. The dealer has a special leasing arrangement where you pay $90 today and $490 per month for the next two years. If you purchase the car, you will pay it off in monthly payments over the next two years at an APR of 7 percent, compounded monthly. You believe that you will be able to sell the car for $18,500 in two years.

What is the present value of purchasing the car?

Explanation / Answer

Down payment = $90

Monthly payment = $490

Total months in 2 years = 12*2 = 24

APR = 7%

Monthly interest rate = 7%/12 = 0.5833%

Sale value of car after two years = 18500

Present value of purchasing the car = 90 + 490*Present value annuity factor(0.5833%,24) - 18500*Present value interest factor(0.5833%,24)

= 90 + 490*22.335 - 18500*0.8697

= 90 + 10944.15 - 16089.45 = (5055.3)

Present value of purchasing the car = (5055.3)

Note:

Dear Student my method of solving this question is right but I think there is mistake in question. Current purchase cost of car is 30500 but total loan amount along with down payment is only 90+490*24 = 11850. Total EMI's along with loan amount should also be equal to 30500 but it is only 11850. So, present value of purchasing the car is negative because sale value of car at the end of 2 years is higher than loan amount.

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