Math 1050 Mortgage Project

Name: Jessica Knox			

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

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

Down Payment: 20,000	Mortgage Amount: 180,900

Part I:  30 year Mortgage
Monthly Payment: Calculate the monthly payment for a 30 year loan (rounding up to the nearest cent) by using the following formula. Show your work. [PMT is the monthly loan payment, P is the mortgage amount, r is the annual percent rate for the loan in decimal, and Y is the number of years to pay off the loan.]  For the 30 year loan use an annual interest rate of 4.975%.

Monthly Payment for a 30 year mortgage: $968.35

Note that this monthly payment covers only the interest and the principal on the loan. It does not cover any insurance or taxes on the property.

Amortization Schedule: In order to summarize all the information regarding the amortization of a loan, construct a schedule that keeps track of the payment number, the principal paid, the interest, 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.net/amortization/amortize.html.  Enter the amount of the loan, i.e. the selling price minus the down payment, the interest rate, and the appropriate number of years.  Check the box to show the schedule.

Amortization Schedule monthly payment for a 30 year mortgage $968.35
(Note: if this is more than 2 or 3 cents different from your calculation, check your numbers!)

Total interest paid over 30 years: $167,706.00

Total amount paid: $348,606.00

Notice that the amount of the payment that goes towards the principal and the amount that goes towards the interest are not constant.  What do you observe about each of these values? As the amount going towards the principle goes up the amount going towards interest goes down,

Number of first payment when more of payment goes toward principal than interest: 194

As already mentioned, these payments are for principal and interest only.  You will also have monthly payments for home insurance and property taxes.  In addition, it is helpful to have money left over for those little luxuries like electricity, running water, and food.  As a wise home owner, you decide that your monthly principal and interest payment should not exceed 35% of your monthly take-home pay.  What minimum monthly take-home pay should you have in order to meet this goal?  

Minimum monthly take home pay = $2766.71

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 gross annual salary will you need to make to have the monthly net salary stated above?  

Minimum gross annual salary = $45480.16

Part II:  Selling the House
Let's suppose that after living in the house for 10 years, you want to sell.  The economy experiences ups and downs, but in general the value of real estate increases over time.  To calculate the value of an investment such as real estate, we use continuously compounded interest.

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.  

Value of home 10 years after purchase: $299,856.76

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

Selling price of your house: $299,856.76

Original down payment $20,100

Mortgage paid over the ten years $116,202.00

The principal balance on your loan after ten years $147,036.48

Do you gain or lose money over the 10 years?  How much?  Show your amounts and summarize your results: Gain. $16,518.28
Down payment: $20,100          Principle Balance: $147,034.48    Selling Price: $299,856.76
Mortgage Paid: $116,202         Amount paid:        $136,302.00     Amount Paid: $283,338.48
                           -----------                                  --------------------                         -----------------
                           $136,302                                        $283,338.48                            $16,518.28

Part III:  15 year Mortgage
Using 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 the nearest cent) by using the following formula. Show your work! [PMT is the monthly loan payment, P is the mortgage amount, r is the annual percent rate for the loan in decimal, and Y is the number of years to pay off the loan.] For the 15 year loan use an annual interest rate of 4.735%.

Monthly Payment for a 15 year mortgage =  $1405.70

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

Amortization Schedule monthly payment for a 15 year mortgage $1405.70
(Note: if this is more than 2 or 3 cents different from your calculation, check your numbers!)

Total interest paid over 15 years: $72,126.00

Total amount paid: $253,026.00

Number of first payment when more of payment goes toward principal than interest 5

Suppose you paid an additional $100 towards the principal each month. How long would it take to pay off the loan with this additional payment and how will this affect the total amount of interest paid on the loan?  [If you are making extra payments towards the principal, include it in the monthly payment and leave the number of payments box blank.]

Length of time to pay off loan with additional payments of $100 per month: 13 yrs. 7 mo.

Total interest paid over the life of the loan with additional $100 monthly payments: $64,741.29

Total amount paid with additional $100 monthly payments: $245,613.29

Compare this total amount paid to the total amount paid without extra monthly payments.  How much more or less would you spend if you made the extra principal payments? $7412.71

Part III: Reflection

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

	After doing this project I can see the good and the bad in both the 15 year and 30 year loan options. I truly don’t think there is any one type of loan that is good for everyone I think it more has to do with a individuals situation and future plans. If you plan to stay in your home long enough to pay it off and you can afford the higher monthly payment then it would defiantly be wiser to go with the 15 year plan. It gets paid off faster and the amount of money you save is substantial. However if your future plans have you moving on from that home into something newer or bigger then I think the 30 year loan is the better option. It has lower monthly payments and you know you are not going to stay so paying it off faster is not a goal.