Math 1050 Mortgage Project

Due date:

In this project we will examine a home loan or mortgage. Assume that you have found a nomefor sale and have agreed to a purchase price of $201,000.

Down Payment: You are going to make a 10% down payment orrthe house. Determine theamount of your down payment and the balance to finance.

Down Payment 10) too, Mortgage Amount_\ <Z:V. 9 0nI

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Part I: 30 year MortgageMonthly Payment: Calculate the monthly payment for a 30 year loan (rounding up to thenearest cent) by using the following formula. Show your work. [PMT is the monthly loanpayment, P is the mortgage amount, r is the annual percent rate for the loan in decimal, and Y isthe number of years to pay off the loan.] For the 30 year loan use an annual interest rate of

J4.975%.

p(f2)1-(1+f2f12Y

Show work here

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1l-Monthly Payment for a 30 year mortgage Cllu<D. "3 GNote that this monthly payment covers only the interest and the principal on the loan. It does notcover' any insurance or taxes on the property.Amortization Schedule: In order to summarize all the information regarding the amortization ofa loan, construct a schedule that keeps track of the payment number, the principal paid, theinterest, and the unpaid balance. A spreadsheet program is an excellent tool to develop an

amortization schedule. We can use a free amortization spreadsheet on the web.The web address is: http://www.bretwhissel.netlamortization/amortize.html. Enter the amountof the loan, i.e. the selling price minus the down payment, the interest rate, and the appropriatenumber of years. Check the box to show the schedule.

Amortization Schedule monthly payment for a 30 year mortgage '"' <1 ~~, ~~(Note: if this is more than 2 or 3' cents different from your calculation, check youF numbers!)

Total interest paid over 30 years 4t \ (01 )1010.00

Total amount paid i 3!...\-&} foo'" .00

Notice that the amount of the payment that goes towards the principal and the amount that goestowards the interest are not constant. What do you observe about each of these values?At fir-0t} -th-e p"'1meVl~ e;[r-£. rnoy.t inl e •....e0t ttla.h prit'luipttll_

The"" CIS \'Y10re of +ht priYlvtpttl IS paJtA aown tyler.e- ofthi pOvij h.+ ~~ ~ to Pt'il'lvipG\.It ,

Number of first payment when more of payment goes toward principal than interest 19LfAs already mentioned, these payments are for principal and interest only. You will also havemonthly payments for home insurance and property taxes. In addition, it is helpful to havemoney left over for those little luxuries like electricity, running water, and food. As. a wise homeowner, you decide that your monthly principal and interest payment should not exceed 35% ofyour monthly take-home pay. What minimum monthly take-home pay should you have in orderto meet this goal? Show your work for making this calculation.

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Minimum monthly take home pay = ~ ~,l (p~ .,1

It is also important to note that your net or take-home pay (after taxes) is less than your gross pay(before taxes). Assuming that your net pay is 73% of your gross pay, what minimum grossannual salary will you need to make to have the monthly net salary stated above? Show yourwork for making this calculation.

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Minimum gross annual salary = '-- eft Lt C1! if bg , i9;

Part II: Selling the HouseLet's suppose that after living in the house for 10 years, you want to sell. The economyexperiences ups and downs, but in general the value of real estate increases over time. Tocalculate the value of an investment such as real estate, we use continuously compoundedinterest.

Find the value of the home 10 years after purchase assuming a continuous interest rate of 4%.Use the full purchase price as the principal. Show your work.

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t: 10

Value of home 10 years after purchase _~ __ ~_q_~_)_<l_~_to_'_l_b

Assuming that you can sell the house for this amount, use the following information to calculateyour gains or losses:

Sell ing price of your house

Original down payment 'J-OJ \ 00

Mortgage paid over the ten years ~s} <:zw3. t;2 .>The principal balance on your loan after ten years \ 41J ~ ~ • ~~

Do you gain or lose money over the 10 years? How much? Show your amounts and summarizeyour results: b Q .C\""ou.~t \eft

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<6'~~!1lPPart III: 15 year MortgageUsing the same purchase price and down payment, we will investigate a 15 year mortgage.

Monthly Payment: Calculate the monthly payment for a 15 year loan (rounding up to thenearest cent) by using the following formula. Show your work! [PMT is the monthly loanpayment, P is the mortgage amount, r is the annual percent rate for the loan in decimal, and Y isthe number of years to pay off the loan.] For the 15 year loan use an annual interest rate of4.735%.

PMT= p(f2)1-(1+f2fI2Y

Show work here.'9>0 ,\OO( . 0 413 5 ~

I \2... )p= 1<60/£100r ~ .04135(:: \5

Monthly Payment for a 15 year mortgage = \\ \ 4 D S.70

Use the amortization spreadsheet on the web again, this time entering the interest rate andnumber of payments for a 15 year loan.

Amortization Schedule monthly payment for a 15 year mortgage \ ) L\ 0 S,10(Note: if this is more than 2 or 3 cents different from your calculation, check your numbers!)

Total interest paid over 15 years "\ 2.) \ 2-\0 .J)O

Total amount paid

Number of first payment when more of payment goes toward principal than interest 5Suppose you paid an additional $100 towards the principal each month. How long would it taketo pay off the loan with this additional payment and how will this affect the total amount ofinterest paid on the loan? [If you are making extra payments towards the principal, include it inthe monthly payment and leave the number of payments box blank.]

Length of time to payoff loan with additional payments of $1 00 per month \ '3. CO 16 'L.et\ noTotal interest paid over the life of the loan with additional $100 monthly payments LP 4- I1\'2>. 2qTotal amount paid with additional $100 monthly payments d-Y5 I lD \ 3. '2,9Compare this total amount paid to the total amount paid without extra monthly payments. Howmuch more or less would you spend if you made the extra principal payments? Vho.~ .l-L.'jtO'" WOIA \&t sptn4 ~ 11.\\'1- 1\ US0 ,f '(OlA 't\IU

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Part III: Reflection

Did this project change the way you think about buying a home? Write one paragraph statingwhat ideas changed and why. If this project did not change the way you think, write how thisproject gave further evidence to support your existing opinion about buying a home. Be specific.

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