Question

Financial Planning Cases

The Johnsons' Credit Questions

They are considering trading their car in for a newer used vehicle so that Harry can have dependable transportation for commuting to work. The couple still owes $5,130 to the credit union for their current car, or $285 per month for the remaining 18 months of the 48-month loan. The trade-in value of this car plus $1,000 that Harry earned from a freelance interior design job should allow the couple to pay off the auto loan and leave $1,250 for a down payment on the newer car. The Johnsons have agreed on a sales price for the newer car of $21,000.

(b) Calculate the monthly payment for a loan period of three, four, five, and six years at 6 percent APR. Describe the relationship between the loan period and the payment amount.

Answer 1

Sale price of new car = $ 21,000

Down payment = $ 1,250

Loan amount = 21,000 - 1,250 = $ 19,750

We can calculate monthly payment for a loan for any period, using PMT function of excel.

Inputs of PM function:

Rate = Interest rate per period = Interest rate per month = APR / 12 = 6% / 12 = 0.5%

Term, N = number of years

nper = number of months in the Term = 12 x N

PV = Present value of loan amount = - $ 19,750

Hence, PMT (Rate, nper, PV)

Please see the table below:

Number of years	N	3	4	5	6
Nper	12 x N	36	48	60	72
Rate		0.50%	0.50%	0.50%	0.50%
PV		(19,750)	(19,750)	(19,750)	(19,750)
Monthly payment	PMT (Nper, Rate, PV)	601	464	382	327

There is an inverse non linear relationship between the loan period and the payment amount.

• As the loan period increases, the monthly payment decreases
• The rate of decline in monthly payment decreases as loan period increases