Question

Lupé made a down payment of $8000 toward the purchase of a new car. To pay the balance of the purchase price, she has secured a loan from her bank at the rate of 5%/year compounded monthly. Under the terms of her finance agreement she is required to make payments of $440/month for 36 months.

What is the cash price of the car? (Round your answer to the nearest cent.)

Answer 1

Mortgage amount		=	Presnt value of annuity of monthly payment
Present Value of annuity			=	P*PVAF(rate,time)
		where P	=	monthly payment=$440
		t	=	time in months=36 months
		r	=	interest rate = r= 0.05/12=0.004167
	calculation of PVAF(0.4167%,36)
	PVAF(rate,time)		=	[1-(1+r)^-n]/r
	PVAF(0.4167%,36)		=	[1-(1+0.004167)^-36]/0.004167
			=	[1-(1.004167)^-36]/0.004167
			=	[1-0.0.860966]/0.004167
			=	0.139034/0.004167
			=	33.3655
Present Value of annuity			=	$440*33.3655
			=	$    14,680.82
cash price of car			=	$8,000+$14,680.82
			=	$    22,680.82
If you have any doubt,please ask
Please upvote the answer