Question

5. You are out shopping for a new car. You have found a Toyota Sienna priced at 34,400. The dealer has told you that if you can come up with a down payment of 3,300, he would be willing to finance the balance at an EAR of 5.65%. for 4 years. You come back home and after doing the math you find that the monthly payment is beyond your means. At this time, you can only afford a monthly payment of $661.01. In order to accomplish that, the dealer will have to offer you a substantially lower APR. So the next day, you tell the dealer that since the demand for Toyotas are substantially lower at this time due to quality control issues, you can only go ahead if the dealer is willing to lower the APR so that the monthly payment is $661.01. What is the monthly payment that is beyond your means at this time? What should be the APR so that the monthly payment is $661.01?

A. $1,892.45 AND 1.99%

B. $786.44 AND 5.51%

C. $723.42 AND 0.99%

D. $989.71 AND 3.99%

Answer 1

		Amount of loan	$        31,100	(34400-3300)
		Monthly payment	$661.01
		Number of instalments	48	(4*12)
		APR	Monthly interest
		1.99%	0.16583333	%
		5.51%	0.45916667	%
		0.99%	0.0825	%
		3.99%	0.3325	%
				(Using PV function of excel, Nper=48,PV=31100,Pmt=661.01)
		Monthly interest rate(Percent)	PV
		0.165833333	$30,474.27
		0.459166667	$28,417.05
		0.0825	$31,095.89
		0.3325	$29,281.16
		Hence at interest rate=0.99% , the PV is equal to the loan amount (Instalment payment $661.01)
		Original offer EAR=5.65%=0.0565
		Monthly interest=r
		(1+r)^12=1.0565
		r=(1.0565^(1/12))-1
		r=	0.00459063
		Monthly payment	$723.40	(Using PMT function of excel with Rate=0.00459063, Nper=48, PV=31100)
		ANSWER:
	C	$723.42 AND0.99%