Question

Chris Jennings is purchasing a home for $180,000 and has been approved for a 20-year fixed rate loan at 3.6% interest compounded monthly. If Chris agrees to pay 25% of the purchase price as a down payment, what is the monthly mortgage payment?

	A.	$263.30
	B.	$384.90
	C.	$613.77
	D.	$789.90
	E.	$1,053.20

Answer 1

Solution:
	Answer is D. $789.90
Working Notes:
	Here we will use concept of present value of annuity of monthly payments.
	present value of annuity = Px[ 1-1 /(1 + i)^n)]/ i
	But before that we have get the loan value which is actual mortgage , as there is down payment of 25% of purchase price . Means out $180,000 is recovered as down payment initial 25% x 180,000 =45,000 balance 180,000 -45,000 =135,000 recovered from monthly payments. hence we will use concept of present value of annuity for this $135,000
	P=monthly mortgage payment = ??
	i= interest rate per period = 3.6%/12
	n= no. Of period = 12 x 20 =240
	PV of annuity= Mortgage loan $135,000   balance of loan after down payment
	present value of annuity = Px[ 1-1 /(1 + i)^n)]/ i
	135,000 = P x (1-1/(1+(3.6%/12))^240)/(3.6%/12)
	135,000 = P x 170.9076059
	P= 135,000/170.9076059
	P= $789.90048
	P= $789.90
Hence	P=monthly mortgage payment = $789.90
Please feel free to ask if anything about above solution in comment section of the question.