Buying a house report
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School
Utah Valley University *
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Course
1030
Subject
Mathematics
Date
Apr 3, 2024
Type
docx
Pages
5
Uploaded by MegaArtWalrus40
Math 1030
Buying a house
Name
sage gross
Select a house from a real estate booklet, newspaper, or website. Find something reasonable – between
$150,000 and $400,000. Copy and paste the picture, brief description, and price of your chosen house here.
This beautifully updated bungalow home nestled right in the heart of Liberty Wells in Salt Lake City. You won't want to miss your opportunity to get into this neighborhood at a great price. This 2 bedroom home offers an open and airy feel. The spacious living room is perfect for entertaining indoors. The beautiful kitchen leads you to the backyard where you
can enjoy the beautiful garden spaces and patio for all of your outdoor entertaining needs. When you're not at home, you can enjoy the all the wonders of the city. From downtown Salt Lake to sugarhouse, all right outside your front door
Assume that you will pay the asking price for your house. The listed selling price is: ___$499,000_____
Assume that you will make a down payment of 20%. Your down payment is __$99800_. The amount of the mortgage is __399200___.
Ask/Research at least two lending institutions for the Annual Percentage Rate (APR) for both a 15-year and a 30-year fixed rate mortgage with no “points” or other variations on the interest rate for the loan.
Name of first lending institution: ____Sage Home Loans Corporation__________
Rate for 15-year mortgage: ___5.572%_____
Rate for a 30-year mortgage: ____6.175%________
Name of second lending institution: ______Homefinity______________
Rate for 15-year mortgage: ___5.500%______
Rate for a 30-year mortgage: _____6.250%________
Assuming that the rates are the only difference between the lending institutions, find the monthly payment at the better interest rate for each type of mortgage.
Which lending institution did you choose for the 15-year mortgage? __Homefinity________
Based on the given APR, calculate the monthly payment. Show your work. Use the given formula.
M=P(r(1+r)^n/((1+r)^n) -1. M
=399200(0.0045833(1+0.0045833)^180)/((1+0.0045833)^1801
=3261.80
Which lending institution did you choose for the 30-year mortgage? ___Sage Home Loans Corporations_______
Based on the given APR, calculate the monthly payment. Show your work. Use the given formula.
M=P(r(1+r)^n/((1+r)^n) -1. M
=399200(0.00514583(1+0.00514583)^360)/((1+0.0045833)^360)-1
399200(0.033947186/5.59716497=399200x0.006071258=2420.60
Conclusion, 15-year monthly payment: __3261.80______
30-year monthly payment: __2438.50______
These payments cover only the interest and the principal on the loan. They do not cover the insurance or taxes.
To organize the information for the amortization of the loan, I constructed a schedule that keeps track of: 1.
payment number and/or the month and year
2.
amount of the payment
3.
amount of interest paid 4.
amount of principal paid
5.
remaining balance. There are other programs online available for this, but a Microsoft Excel worksheet that does this is provided for you in Canvas. Fill in the sample of payments in the following schedules and answer the questions after each section.
15-year mortgage
Payment Payment Date
Payment Interest Paid Principal Paid Remaining
Number
Amount ($)
($)
($)
Balance ($)
1.
1
1/1/2019
3261.80
1829.67
1431.13
397767.87
2.
2/1/2019
3261.80
1823.10
1438.69
396329.18
50.
2/1/2023
3261.80
1469.97
1791.80
318929.86
90.
6/1/2026
3261.80
1110.33
2151.46
240103.25
120.
12/1/2028
3261.80
793.98
2467.82
170764.33
150.
6/1/2031
3261.80
431.11
2830.69
91229.61
180.
12/1/2033
3261.80
14.88
3246.92
0
Total
-------------------
-------------------
Please answer the following questions by selecting the best option for each of the questions:
1.
The total principle paid is the same as the ___a____ .
a.
payment amount times the number of payments.
b.
amount of the loan.
c.
interest paid on the house.
d.
cost of the house.
2.
The total amount paid is the number of payments times ______c_____.
a.
the interest paid.
b.
the down-payment.
c.
the monthly payment amount.
d.
the interest rate.
3.
The total interest paid is the total amount paid minus ____a____ .
a.
the amount of the loan or principal.
b.
the down-payment.
c.
the interest rate times the principal.
d.
the closing costs.
Answer the questions by using the proper numbers to fill in the blanks. Cross out any improper words in the parenthesis. You are comparing the total amount of interest paid on the 15-year mortgage at the end of the loan to the principal of the loan. Refer to the excel sheet, if needed. 1.
Payment number __30_ is the first one in which the principal paid is greater than the interest paid.
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2.
The total amount of interest is $___187923.49___ (less ) than the principal.
3.
The total amount of interest is _____59.2 % (less) than the principal.
4.
The total amount of interest is ____47.08______ % of the principal.
30-year mortgage
Payment Number
Payment Date
Payment Amount ($)
Interest Paid ($)
Principal Paid ($)
Remaining Balance ($)
1.
1/1/2019
2438.50
$2,054.22
$384.29
$398,815.71
2.
2/1/2019
2438.50
$2,052.24
$386.26
$398,429.45
60.
12/1/2023
2438.50
$1,918.30
$520.20
$372,267.35
120.
12/1/2028
2438.50
$1,730.69
$707.81
$335,621.58
240.
12/1/2028
2438.50
$1,128.10
$1,310.40
$217,915.50
300.
12/1/2043
2438.50
$655.51
$1,782.99
$125,603.62
360.
12/1/2048
2438.50
$12.48
$2,426.02
0.00
Total
-------------------
-------------------
Answer the questions by using the proper numbers to fill in the blanks. Cross out any improper words in the parenthesis. You are comparing the total amount of interest paid on the 30-year mortgage at the end of the loan to the principal. Refer to the excel sheet, if needed.
1.
Payment number __240__ is the first one in which the principal paid is greater than the interest paid.
2.
The total amount of interest is $_____877861.36____ (more) than the principal.
3.
The total amount of interest is ____119.79_______ % (more) than the principal.
4.
The total amount of interest is __219.7______ % of the principal.
Suppose that you paid an additional $100 a month:
Refer to the third set of columns in the spreadsheet. You will notice that $100 was added to the 30-
year monthly payment. If you look down the columns, you will notice that at some point the values turn negative. Due to everyone’s house prices and interest rates being different, there are more rows than needed to do the calculations. Therefore, you will need to calculate the totals to help you answer the following questions. There is a video to walk you through these steps. 1.
The total amount of interest paid with the $100 monthly increase would be $___449160.40________
2.
The total amount of interest paid with the $100 monthly increase would be $___________34000_____ (more or less) that the interest paid for the regular payments only.
3.
The total amount of interest paid with the $100 monthly increase would be ___8.19_____________
% (more or less) that the interest paid for the scheduled payments only.
4.
The $100 monthly increase would pay off the mortgage in __8__ years and _6___ months; that’s _78___ months sooner than paying only the scheduled payments.
Observations and reflections:
Summarize what you have done and learned on this project. Because this is a math project, you must compute and compare numbers
, both absolute and relative values
, which have not been compared above. Statements such as “a lot more” and “a lot less” do not have meaning in this class. Make the necessary computations and compare:
1.
The 15-year monthly mortgage payment to the 30-year monthly mortgage payment Monthly payment wise I like the 30 year better because you are paying less each month so your expenses are lower
2.
The 15-year mortgage interest to the 30-year mortgage interest
Interest wise I would say I like the 15 year you save a lot of money on the smaller interest rates and you pay it off. Faster. 3.
The 15-year mortgage to the 30-year mortgage with extra payment
I like the 15 month better, you just pay it off so quickly and it just makes it seem so worth it. 4.
Comment on other factors (specifically regarding mortgages) that buyers must consider when purchasing a home.
I would consider what is in your budget and what you can afford. Definitely do a cost analysis before hand.