Math 114 15 vs 30 year mortage project
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Liberty University *
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Course
114
Subject
Mathematics
Date
Feb 20, 2024
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docx
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Uploaded by ChancellorOstrich3788
MATH 114
P
ROJECT
1 I
NSTRUCTIONS
Topic – Mortgages: 15-year vs. 30-year Round answers for problems 1-2 to the nearest cent
1.
Say that a family is purchasing a house with a $230,000 mortgage and an annual interest rate of 5%. The size of their monthly payment will depend on the term of the mortgage.
The Excel function “pmt” can be used to compute these monthly mortgage payments. The 3 arguments of function “pmt” are: 1) the monthly interest rate (0.05/12); 2) the total number of monthly payments; and 3) the mortgage amount. (12 pts)
a.
Find the monthly payments if the $230,000 was financed over 15 years. $1,818.83
b.
Find the monthly payments if the $230,000 was financed over 30 years. $1,234.69
c.
Multiply your answer to part (a) by the number of payments to find how much the
family would need to pay in total over the life of the 15-year loan. Subtract the principal amount from this to give the amount of interest paid over the life of the loan. $97,389.40
d.
Multiply your answer to part (b) by the number of payments to find how much the
family would need to pay in total over the life of the 30-year loan. Subtract the principal amount from this to give the amount of interest paid over the life of the loan. $214,488.40
2.
A standard rule for lenders is that a family’s house payment should not exceed 28% of their monthly income. For a family making $7000 per month, this would equate to $1960 per month. Assuming that $260 out of this monthly payment would go to pay their property tax and homeowner’s insurance, this would allow for the remaining $1700 of their monthly payment to repay their mortgage. Given this monthly mortgage payment of
$1700, find the size of the mortgage a family could afford using the Excel function “pv”. This function finds the present value of the loan for various mortgage terms and interest rates. The 3 arguments of function “pv” are: 1) the monthly interest rate; 2) the total number of payments; and 3) the amount of each payment. (4 pts)
a.
Assuming a $1700 monthly payment, find the mortgage that a family could afford
at an annual interest rate 5% for a 15-year mortgage. $339,947.83
b.
Assuming a $1700 monthly payment, find the mortgage that a family could afford
at an annual interest rate 5% for a 30-year mortgage
. $339,999.99
=pv (rate, nper (number of paymentsbb), pmt)
Page 1 of 2
MATH 114
3.
Based on your answers to questions 1 and 2, what is the advantage of having a 15-year mortgage, and what is the advantage of having a 30-year mortgage? Which option do you think is wiser? Please respond using at least 100 words. (4 pts)
If you choose a thirty year mortage you are paying less per month than you would if you had a fifteen year mortage because the intention is that it takes you longer to pay off. While choosing the thirty year mortage saves you more money per month you are ultimately paying more overall than you would if you had chosen to do a fifteen year mortage because the price gap per month does not make up for the doubled amount of time between the mortages. So even though the thirty year mortage saves you more money per month which may make the payments more achievable for families it’s the fifteen year mortage that is the most financialy smart decision long term.
4.
Proverbs 22:7 says, “The rich rules over the poor, and the borrower is the slave of the lender.” In light of this verse, and the Bible’s more general teaching on debt, many Christians have counselled that incurring excessive debt is undesirable. As financial expert Dave Ramsey puts it: “If you must take out a mortgage, pretend only 15-year mortgages exist.” Discuss how you would apply the Bible’s warning about borrowing when deciding how to go about purchasing a home. Does the Bible prohibit any kind of borrowing? Does it influence which type of mortgage is more attractive? Or does it not really apply to this type of loan? Please provide a response of at least 100 words. (5 pts)
Based on Proverbs 22:7 I believe picking a 15 year mortage over a 30 year mortage would better follow the bibles teaching because its less money that you are paying, making you a “slave” for a lesser amount of time. Being in debt for a larger amount of time can influence you to become more “one track minded” which is directed towards paying back your debts rather than focusing your eyes and goals upon God. The Bible does warn against debt but it never condems those who sin or say that it is wrong. While it may be okay and not sinful that does not mean that you should not be financially wise in the decisions that you make when it comes to debt. Life decisions, big or small such as this one should be brought before the Lord in prayer before making a final decision on the matter. Page 2 of 2
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