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?

Solutions

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

Next > < Previous

Related Solutions

Judy recently purchased her first home for $220,000. She made a down payment of $20,000, and...

Judy recently purchased her first home for $220,000. She made a down payment of $20,000, and financed the balance over 15 years, at 6% interest. How much is her principal and interest payment each month?

Miguel recently purchased his first home. He is very excited about making improvements to the home....

Miguel recently purchased his first home. He is very excited about making improvements to the home. He decides it would be cheaper if he had his own water source so he digs a well in his backyard. Next he decides to construct a large building right next to the edge of his property. The following spring, Miguel gets a letter from his neighbor Stephen claiming Miguel has stolen Stephen's water source by digging a well. Miguel decides not to say...

You and your family have recently closed on the purchase of your first home and you...

You and your family have recently closed on the purchase of your first home and you are excited. You are in need of furniture and appliances for your new home. You have decided to purchase some of the items from eBay and have found a dining room set and living room furniture from a private seller on eBay’s website. You look at the pictures on the website and notify the seller through email that you would like to purchase these...

Your are comparing two options for a home mortgage. The first option is a 15-year mortgage...

Your are comparing two options for a home mortgage. The first option is a 15-year mortgage with a 3.75% annual rate, and the second option is a 30-year mortgage with a 4% interest rate for a 500,000 loan. If you want your monthly payment under the first option to be the same as the monthly payment under the 30-year option, how much additional down payment will you neet to put dow under the 15-year option?

Suppose you have just purchased your first home for $300,000. At the time of purchase you could afford to commit 20% of the purchase price to a down-payment

Suppose you have just purchased your first home for $300,000. At the time of purchase you could afford to commit 20% of the purchase price to a down-payment. Suppose over time you paid down the principal of the loan to $220,000 and at that point in time you can no longer make any mortgage payments (i.e., you default on the loan). If the lender were to foreclose on your property and sell it for $190,000, determine the amount of the...

The price of a home is $240 000. The bank requires a 15% down payment. The...

The price of a home is $240 000. The bank requires a 15% down payment. The buyer is offered two mortgage options: 15-year fixed at 8.5% or 30-year fixed at 8.5%. Calculate the amount of interest paid for each option. How much does the buyer save in interest with the 15-year option? Use the following formula to determine the regular payment amount. Find the monthly payment for the 15-year option. $ nothing (Round to the nearest dollar as needed.) Find...

A home is purchased for 395,000 with a 10% down payment and a 30 year amortized...

A home is purchased for 395,000 with a 10% down payment and a 30 year amortized mortgage charging 3.6% compounded monthly find: a) the amount borrowed, b) the size of the monthly mortgage payment and c) the total interest paid over 30 years?

Persuasive Claim: Double Payment for Air Conditioner Your company recently purchased a Solana Model AC400 window...

Persuasive Claim: Double Payment for Air Conditioner Your company recently purchased a Solana Model AC400 window air conditioner for your small business office. At the time of the purchase, the salesperson wrote up the bill for the wrong unit. You discovered the error, and the clerk cancelled the initial credit entry and wrote a new charge slip. Months later in looking over the bills, you noticed that your company had paid two bills for an air conditioner: one for the...

Patricia purchased a home on January 1, 2017 for $1,250,000 by making a down payment of...

Patricia purchased a home on January 1, 2017 for $1,250,000 by making a down payment of $100,000 and financing the remaining $1,150,000 with a 30-year loan, secured by the residence, at 6 percent. During 2017-2019, Patricia made interest-only payments on the loan of $69,000. What amount of the $69,000 interest expense that Patricia paid during 2019 may she deduct as an itemized deduction? a - $0 b - $9,000 c - $60,000 d - $69,000

Rick Rueta purchased a $88,000 home at 7.5% for 30 years with a down payment of...

Rick Rueta purchased a $88,000 home at 7.5% for 30 years with a down payment of $25,000. His annual real estate tax is $1,932 along with an annual insurance premium of $1,092. Rick’s bank requires that his monthly payment include an escrow deposit for the tax and insurance. What is the total payment each month for Rick? (Round your answer to the nearest cent.)

Subjects