Question

Suppose that you have two alternatives to purchase a new Mini Cooper. You must put $2500 down, and make payments of $387 per month for 48 months, at the end of each month, or pay $19,000 cash. The dealer's stated financing rate is 5.1% APR. If you pay cash for the car, how much money are you saving (+) or losing (-) in comparison with financing your purchase through the dealer? (Your answer should be positive when saving money, negative when you are paying more.)

Answer 1

You can purchase a Mini Cooper through either ways, you pay $2500 down and pay monthly payment at the end of each month for 48 months which is $387 or pay $19,000 cash now

- Calculating the Present Value today of monthly Payment:-

Where, C= Periodic Monthly Payments = 387

r = Periodic Interest rate = 5.1%/12 = 0.425%

n= no of periods = 48   

Present Value = $16,771.67

So, Value today of future periodic monthly payment is $16,771.67

Total Value of purchase car today = Present Value + Down Payment = $16,771.67 + $2500

= $19,271.67

- If you purchase in cash you have to pay $19,000

If you agreee to financing terms, you will lose money by paying as the Value today of financing term is higher than paying cash today

Thus, Amount of Losing money = $19,000 - $19,271.67

Amount of Losing money = -$271.67

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