after graduating, you need a new car and the dealer has offered you a price of $
ID: 2779816 • Letter: A
Question
after graduating, you need a new car and the dealer has offered you a price of $20,000, with the following payment options:
A) pay cash and receive a $2,000 rebate, making the price of the car $18,000. This means you will be financing $18,000 somehow to take advantage of this offer and pay the dealer.
B) pay a $5,000 down payment and finance the remaining $15,000 with a 0% APR loan over 30 months. Just finishing your MBA Program, you are in debt and you expect to be in debt for at least the next 2.5 years, including debt from the purchase of the new car. You plan to use credit cards to pay your expenses; luckily you have one with a low (fixed) rate of 15% APR (monthly). Which payment option is best for you? (Hint: how much will you pay for the $5,000 over 30 months?
C) Explain in a sentence or two if you think the 15% is a "real" or a nominal/market rate of interest and why?
***Figure out how much money are you going to pay out for a loan of $18,000 at 15% APR. Then, figure out how much money are you going to pay out for a loan of $5000 at 15% APR for 30 months + $15,000 interest free. The lower of the two amounts is the winner!
Explanation / Answer
Given:
Solution:
A. Option 1: To make full payment of $20,000 by cash and receive a rebate of $2000
Car Payment = $20,000 - $2,000
= $18,000
B. Option 2: To pay a $5,000 down payment and finance the remaining $15,000 with a 0% APR loan over 30 months.
i.e., an initial payment of $5,000 and 30 monthly payments of $500 thereafter.
0% APR offer means that you won't have to pay interest on your purchases for a specific time period. Depending on the credit card offer, the 0% APR can last anywhere from six months to over a year.
The cost of the car under dealer financing is:
r six month = 15% / 12 = 1.25%
Present Value (PV) = Initial Value + Present Value of Annuity
= $5,000 + [$500/1.25%(1-(1/1.0125)30)]
= $5,000 + $12,444.45
Car Payment (PV) = $17,444.45
Hence, Option 2 is best for ABC’s Car Payment!
C. 15% is nominal rate of interest. Generally, the nominal interest rate is also known as an Annualised Percentage Rate or APR which is defined as the periodic interest rate multiplied by the number of periods per year. (See cost of the car calculation for reference)
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