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Home Mortgages College Algebra The work on this project is to be
YOUR OWN! The teaching assistants will check your #1 3 to ensure
you are on the right track with the formula. You would need to
email your TA with your answers to 1 3 for them to check. They will
NOT check the Dropbox except to grade the finished projects. We
will use Turnitin to verify if parts of the project are taken from
someone else or another source. If your project is seen as being
copied from another student you will receive a 0 on it and could
possibly receive an XF for the entire course.
While you may not be in the market for a home right now, it is
probably an event that will occur for you sometime in the future.
The formula below gives the monthly payment P required to pay off a
loan L at an annual rate of interest r, expressed as a decimal, but
usually given as a percent. The time t, measured in months is the
duration of the loan, so a 15 year mortgage requires t = 12 15 =
180 monthly payments. On March 15, 2013, the average interest rates
were: (a) 4.28% on 30-year mortgages (b) 3.4% on 15-year mortgages
1. For each of these loans, calculate the monthly payment for a
loan of $125,000. All answers should be rounded to the nearest
hundredth since you will be dealing with money. It is important
that you do not round until your final answer due to round off
errors. 2. Then compute the total amount paid over the term of the
loan. 3. Finally, calculate the interest paid.
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On September 1, 2013, the average interest rates were: (a) 3.6%
on 30-year mortgages (b) 2.88% on 15-year mortgages 4. For each of
these loans, calculate the monthly payment for a loan of $150,000.
5. Then compute the total amount paid over the term of the loan. 6.
Finally, calculate the interest paid.
On March 15, 2013, the average adjustable interest rate (ARM)
was 2.8%. The adjustable rate is linked to an economic index. The
interest rates, and your payments, are periodically adjusted up or
down as the economic index fluctuates. This rate is often fixed for
a period of time. Most home buyers decide to refinance at the fixed
rate because it can go up by as much as 6%. 7. The first 5 years of
an ARM has an interest rate of 2.8%. Calculate what the monthly
payment would be for the first 5 years on a loan amount of
$125,000. When you calculate your monthly payment, you will assume
that the loan is amortized, or calculated, for 30 years. Make sure
you plug in a t value representing 30 years.
After the first 5 years, the interest rate will begin to
fluctuate with the market, so it is a good time to refinance your
loan at a fixed interest rate. Your monthly payments with the ARM
went to paying the interest and the principle on the loan and you
have a new loan balance of $110,723.49. It will cost you $3000 to
refinance. You can refinance your new balance + $3000 refinance fee
at 4.5% fixed interest rate. 8. Calculate the next 25 years monthly
payment on the remaining balance of the house + refinance fee, at a
4.5% interest rate. Make sure you plug in a t value representing 25
years. 9. Compute the total amount paid over the 30 year loan. 10.
Was it more beneficial to do an ARM with this cost added? Explain
your answer.
11. Solve the equation for L. 12. Assume you can afford to pay
$750 per month for a mortgage payment, calculate the amount you can
borrow on March 15, 2013. (a) on a 30-year mortgage. (b) on a
15-year mortgage.
13. Check with your local lending institutions for current rates
for 30-year mortgage, 15-year mortgage, and a three-year ARM.
Choose ONE of these and calculate how much you can borrow with a
$750 per month payment. Please list which lending institution you
obtained your information from.
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14. How much can you borrow if you can afford a payment of $1100
per month with the information you used in Problem 13. 15.
Calculate a couple of the previous problems and round the values,
resulting in a round-off error. Discuss the difference that you
will get per month, per year, and over the time of the loan with
errors in rounding. 16. Lets say that you chose to purchase points
to buy down the interest rate of a $140,000 house. Check out this
website for more information on buying down points:
https://www.bankofamerica.com/home-loans/mortgage/budgeting-for-home/buying-mortgage-points-lower-rate.go
or http://www.investopedia.com/articles/pf/06/payingforpoints.asp
Use the information from March 15, 2013 on a 30 year loan. Lets say
you were going to be in the house for only 10 years, is it to your
advantage to buy 2 points on the loan? Explain your reasoning
mathematically. What is the break even point
(http://www.lendingtree.com/smartborrower/glossary/b/break-even-point/
) of buying down 2 points or leaving the loan as is? It may be
helpful to graph the information so that you can see when this is
going to happen. There is a document in the Doc Sharing tab that
explains how you can insert graphs into text documents using
graphing software available online. 17. Using the rate information
for September 1, 2013, calculate a 30 year loan for $150,000 if you
had $15,000 as a down payment. What was the difference in payments
per month? Do the same for the 15 year loan and calculate the
difference in payment per month? 18. Do you think that the interest
rate plays an important role in determining how much you can afford
to pay for a house? Why or why not? 19. Comment on the three types
of mortgages: 30-year, 15-year, and one-year ARMs. Which would you
take? Why?
SOLUTIONS
1. a)
= $ ( . + . ) = $ . 2. a) Total amount paid = $ . = $ 3. a)
Interest paid = $ $ = $ 1. b)
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= $ ( . + . ) = $ . 2. b) Total amount paid = $ . = $ . 3. b)
Interest paid = $ . $ = $ .
4. a)
= $ ( . + . ) = $ . 5. a) Total amount paid = $ . = $ .
6. a) Interest paid = $ . $ = $ .
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4. b) = $ ( . + . ) = $ . 5. b)Total amount paid = $ . = $ . 6.
b) Interest paid = $ . $ = $ .
7.
Monthly payment during the first 5 years, at the rate of
2.8%
= $ ( . + . ) = $ .
8. Balance at the end of 5 years = $. Refinance fees = $. Total
outstanding balance at the end of 5 years = $. Monthly payment for
the next 25 years, at the fixed rate of 4.5%
= $ . ( . + . ) = $ .
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9. Total amount paid over the 30-year loan = $. + $. = $.
10. At the fixed rate of 6% from the beginning,
Monthly payment for the whole of 30 years would be
= $ ( . + . ) = $ . Total amount paid over the 30-year loan = $.
= $. This is greater than the ARM payments by about $49347.
Therefore, it is beneficial to do an ARM.
11.
= [ + ] = [ + ]
= ( + )
12. a) Loan eligibility on a 30-year mortgage as on March 15,
2013
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= $ + . . = $. b) Loan eligibility on 15-year mortgage as on
March 15, 2013
= $ + . 8. = $.
13.
Name of the Institution Interest rates for 30-
year mortgage
Interest rates for 15-
year mortgage
Interest rates for a
3/1 ARM
Bank of America,
Richmond, KY branch
4.00% 3.13% 2.60%
Sebonic financial 4.00 % 3.00% 2.55%
e-rates mortgage 4.10% 3.10% 2.60%
Considering that Bank of America is my preferred institution to
take loans from,
a) Loan eligibility on a 30-year mortgage as on Apr 15, 2015
= $ + . . = $ b) Loan eligibility on 15-year mortgage as on Apr
15, 2015
= $ + . 8. = $
c) Loan eligibility on 3-year ARM as on Apr 15 2015, considering
the total length of loan to be 30
years,
= $ + . . = $
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14. a) Loan eligibility on a 30-year mortgage as on Apr 15,
2015
= $ + . . = $ b) Loan eligibility on 15-year mortgage as on Apr
15, 2015
= $ + . 8. = $
c) Loan eligibility on a 3-year ARM as on Apr 15 2015,
considering the total length of loan to be 30
years,
= $ + . . = $
15.
a) Calculation of rounding error for problem 8
Difference in monthly payment = $ . $ = $. Difference in yearly
payment = $. $ = $. Difference in total amount paid over the
remaining 25-year of the loan period = $. $ = $.
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b) Calculation of rounding error for problem 10
Difference in monthly payment = $. $ = $. Difference in yearly
payment = $. $ = $. Difference in total amount paid over the
30-year loan period = $. $ = $.
16. Let, the cost of buying points be 10% of the loan amount and
the interest rate rebate be 0.125%
per point.
The cost-benefits analysis is illustrated in the following
table:
Loan amount = $140000
Cost of each point = $1400, cost of two points = $2800
Zero points Two points
Cost per point $0 $2800
Interest rate (%) 4.28 4.03
Monthly payment $691.18 $670.81
Monthly payment savings $0 $20.37
Break even point (months) n/a 137.4
Total savings in the life of the
loan
$0 $4533.86
The graph:
Considering the fact that I am going to be in the house for 10
years, it is not beneficial for me to buy
2 points, because the break even point appears at 137.4 months,
that is, beyond 10 years.
0
500
1000
1500
2000
2500
3000
3500
0 50 100 150 200
Cu
mu
lati
ve
mo
nth
ly p
ay
me
nt
red
uct
ion
($)
Months
Datenreihen1
buy points
Linear (Datenreihen1)
Linear (buy points)
Break-even point
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17. Using the rate information for September 1, 2013
For a 30-year mortgaged loan,
= $ $ ( . + . ) = $ . Difference in monthly payment = $. $ . =
$.
For a 15-year mortgaged loan,
= $ $ ( . + . ) = $ . Difference in monthly payment = $. $ . =
$.
18. Interest rate definitely plays an important part in
determining how much can I afford to pay a
house. For example, other conditions remaining unchanged, the
loan eligibility in problem 13 a) is
$157096, whereas, when the rate of interest falls by 0.25%, the
eligible amount rises to $161947,
which is higher by about $5000.
19. The 30-year mortgage loan is better if sufficient period for
repayment is available. If there is not
sufficient repayment period, 15-year mortgage is preferable. ARM
terms offer initial low rates of
interest and are better if the market is going to be heading
towards lower interest rates, or if
someone is not obliged to keep his or her income down.
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If I have a longer repayment period and the market rates are
expected to vary abruptly, I would go
for a 30-year fixed rate. If I do not have such a long repayment
opportunity and the market remains
volatile, 15-year fixed rate will be my preferred option.
If however, the market rate is relatively stable, I would go for
ARM, because the initial low rate
offers excellent saving opportunities.
