Question

Prof. Finance decides to buy a Nissan Maxima. After paying a down payment and taxes, Prof. Finance can finance the rest of the purchase price with a loan of $28,000 for 60 months at a special finance rate offered by Nissan of 0.9% APR compounded monthly. He finds out that Nissan has a second offer of $2250 cash back (rebate) in place of the special 0.9% finance rate offered. Prof. Finance finds he can get 3.39% APR compounded monthly financing online for 60 months if he takes the $2250 cash back offer. The $2250 cash back would be used as an additional down payment reducing the loan amount.

What is the effective annual rate for each loan option?

Answer 1

Solution: Workings of both the options are as under, Kindly provide necessary feedback with thumbs up or thumbs down.

	Decision to Buy Nissan Maxima
Option 1:	Borrowing of $28,000.00 for 60 months at 0.9% APR compounded monthly
We would use Present Value Annuity Formula to find the Annuity Payment for this option
We know in our case:			Present Value		28000
			Time		60
			Rate (Compunded)		0.075%	0.9% divided by 12
	PVAIF =	Annuity*[1-(1+r)^-n]/r
	28000=	A*48.173
	A=	=28000/48.173		581.24
Thus monthly repayment in option 1 = $581.24
Effective Rate of Interest = (1+r/no of months in a year)^60 - 1
ERI	=(1+0.075%)^60 - 1
	4.601%
Option 2:	Borrowing of $28,000.00 for 60 months at 3.39% APR compounded monthly with cash back of $2250.00
We would use Present Value Annuity Formula to find the Annuity Payment for this option
We know in our case:			Present Value		25750
			Time		60
			Rate (Compunded)		0.283%	3.39% divided by 12
	PVAIF =	Annuity*[1-(1+r)^-n]/r
	25750=	A*55.111
	A=	=25750/55.111		508.07
Thus monthly repayment in option 2 = $508.07
Effective Rate of Interest = (1+r/no of months in a year)^60 - 1
ERI	=(1+0.283%)^60 - 1
	18.478%