Question

You are considering buying a new car worth $25,000 today. The dealership will allow you to pick the car today and pay nothing until after you graduate in four years. After four years, you will make a lumpsum payment. You have two financing options. 1) let the dealership finance it for you or 2) finance it yourself though your investment at a local credit union that earns 8% per year. If you do a dealer financing, you will finance the loan for 4 years at 6% per year compounded monthly. If you choose this option, the dealer will throw in a 10% discount and hence you will only take a loan of 90% of the value of the car. You will do a onetime lumpsum payment to the dealer after 4 years. If you finance it yourself, you will pay additional $4,000 to the original value of the car at the time of payment. This means you will end up paying $29,000 to the dealership if you do not finance with them. You currently have a balance of $21,050 in your investment account at the credit union. Which option will you take

Answer 1

Purchase of a New Car Worth $25,000

Based on the above calculations, it will be more profitable to pay through the dealership than through the investment account and additional borrowing, with a future value gain of $11,226 ($38,812 - $28,586)

Step-by-step explanation:

a) Data and Calculations:

Present value of the new car = $25,000

Interest rate per month = 0.5% (6%/12)

Interest rate per year through self-finance = 8%

Amount to be paid after discount= $22,500 ($25,000*90%)

Amount to be paid through self-fiance = $29,000

Future value to be paid to the dealership in four years = $28,586

Future value of the Investment account of $21,050 after 4 years:

Future value factor = 1.360 (8% per year for 4 years)

Future value = $28,628 ($21,050 * 1.360)

Future value of excess funding required to self-finance = $10,812 ($29,000 - $21,050) * 1.360

Total cost of self-finance = $39,812 ($29,000 + 10,812)

Total cost through dealership 28,586

Difference $11,226

Future value to be paid to the dealership in 4 years from an online financial calculator:

N (# of periods) = 48 (4 * 12)

I/Y (Interest per year) = 0.5 (6%/12)

PV (Present Value) = $22500

PMT (Periodic Payment) = 0

Results

FV = $28,586.01

Total Interest $6,086.01