Your clients recently purchased their first home for $329,000 on August 15, with the first payment...

Your clients recently purchased their first home for $329,000 on August 15, with the first payment due September 15. They made a downpayment of 20% and financed the balance over 30 years at an annual interest rate of 4.49%.

a. What is their monthly mortgage payment?

b. How much interest will they end up paying over the life of the loan?

Expert Solution

Solution:
a.	monthly mortgage payment = $1,332.03 or $1,332
b.	interest will they end up paying over the life of the loan = $216,331.63 or $216,332

Notes:	As there is no details of decimal to be taken in intermediated computation and final answer . I m not rounded of any intermediated computation and given final answer is whole number and in two decimal. If other instruction there please comment I will revert back soon.



Working Notes:

a.	The total value of loan is the sum of 1st present value of annuity of 30 years monthly payments at 4.49% interest rate and down payments and 2nd Down payment


	1st Present value annuity of all the payment made monthly payments for 30 years.
	we get monthly payments first

	Balance of loan net of down payment = Total loan amount - down payment
	Balance of loan net of down payment = Total loan amount - 20% x loan amount
	Balance of loan net of down payment = $329,000 - 20% x $329,000
	Balance of loan net of down payment = $329,000 - $65,800
	Balance of loan net of down payment = $263,200

	Down payment is already paid at initial stage.

So	Balance of loan net of down payment = present value of annuity of monthly payments

	present value of annuity = Px (1-1 /(1 + i)^n)/ i

	P=monthly payment = ??
	i= interest rate per period = 4.49%/12
	n= no. Of period = no of years x no of months in a year = 30 x 12 =360

	PV of annuity= Balance of loan net of down payment =$263,200

	present value of annuity = Px[ 1-1 /(1 + i)^n]/ i
	$263,200 =P X (1-1/(1+ (4.49%/12))^360)/(4.49%/12)
	$263,200 =P X 197.5928036593170
	P= $263,200/197.5928036593170
	P= $1332.032
	=$1,332.03

b.	Interest will they end up paying over the life of the loan is equals to total payment made during life of loan i.e. the monthly payments minus Balance of loan net of down payment or present value of annuity



	Interest will they end up paying over the life of the loan
	= the monthly payments payment during life of loan - Balance of loan net of down payment
	= (360 x monthly payment) - $263,200
	= (360 x ($263,200/197.5928036593170) ) - $263,200
	= 479,531.633973- $263,200
	=216331.633973
	=$216,331.63

	Please feel free to ask if anything about above solution in comment section of the question.

jeff jeffy answered 1 year ago

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