Let’s say that you are now three years into your $30,000 car loan from the previous section and you decide to sell the car. When you sell the car, you will need to pay whatever the remaining balance is on your car loan. After 36 months of payments, how much do you still owe on your car loan?

Question

Accepted Answer

PLAN
We have already determined that the monthly payments on the loan are $590.50. The remaining balance on the loan is the present value of the remaining two years, or 24 months, of payments. Thus, we can just use the annuity formula with the monthly rate of 0.5625%, a monthly payment of $590.50, and 24 months remaining.

EXECUTE

Balance with 24 months remaining [latex] =\$590.50 imes \frac{1}{0.005625} (1-\frac{1}{1.005625^{24} } )=\$13.222.32 [/latex]

Thus, after three years, you owe $13,222.32 on the loan.

Using a financial calculator or spreadsheet:

	N	I/Y	PV	PMT	FV
Given	24	0.5625		-590.5	0
Solve for			13,222.32
Excel Formula = PV(RATE,NPER,PMT,FV)=PV(0.005625,24,-590.50,0)

You could also compute this as the FV of the original loan amount after deducting payments:

	N	I/Y	PV	PMT	FV
Given	36	0.5625	30,000	-590.5
Solve for					13,222.56
Excel Formula = FV(RATE,NPER,PMT,PV)=FV(0.005625,36,-590.50,30000)

The 24 cent difference is due to rounding on the payment amount.

EVALUATE

At any point in time, including when you first take out the loan, you can calculate the balance of the loan as the present value of your remaining payments. Recall that when the bank gave you the $30,000 in the first place, it was willing to take 60 monthly payments of $590.50 in return only because the present value of those payments was equivalent to the cash it was giving you. Any time that you want to end the loan, the bank will charge you a lump sum equal to the present value of what it would receive if you continued making your payments as planned. As the second approach shows, the amount you owe can also be thought of as the future value of the original amount borrowed after deducting payments made along the way.

Question 5.3: Let’s say that you are now three years into your $30,000 car...

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