Question

Edward Nygma is offered the following terms for a car he is considering purchasing: $5,000 down (today) and $400 per month for 6 years. If a fair interest rate for car loans is 4%, what is the price of the car implied by the offer to Nymga

Answer 1

PV of annuity for making monthly payment
P = PMT x (((1-(1 + r) ^- n)) / i)
Where:
P = the present value of an annuity stream	To be computed
PMT = the dollar amount of each annuity payment	$       4,800	400*12
r = the effective interest rate (also known as the discount rate)	4.07%	((1+4%/12)^12)-1)
i=nominal Interest rate	4.00%
n = the number of periods in which payments will be made	6	years
PV of installments=	PMT x (((1-(1 + r) ^- n)) / i)
PV of installments=	4800*(((1-(1 + 4.07%) ^- 6)) / 4%)
PV of installments=	$25,566.97
Down payment=	$       5,000
Total cash price=	5000+25566.97
Total cash price=	$30,566.97