Name: Clay Boitnott
Due date: November 5th 2012
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____$20,100.00__________
Mortgage Amount_____$180,900.00_____________
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%.
PM T =
P(R/12)
———————-
1-(1+R/12)^-12Y
Show work here
180900(.04975/12)=749.98125
1-(1+.04975/12)^-12×30=0.774495394
749.98125/0.774495394=968.3482378
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___$167,704.44_________
Total amount paid _$348,604.44____________
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?
Early on, most of the payment went towards the interest. After a point, the payments start to go primarily towards the principal.
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? Show your work for making this calculation.
Show work here
35%=968.35
968.35/35=27.66714286=1%
27.66714286×100=2766.714286
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? Show your work for making this calculation.
Show work here.
73%=2766.71
2766.71/73=37.90013699=1%
37.90013699×100=3790.013699=minimum monthly gross
3790.013699×12=45480.16438
Minimum gross annual salary = $45,480.16__________________________
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. Show your work.
Show work here.
201000e^.04×10
201000e^.4=299856.7642
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 ___$20,100.00_____________
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:
By subtracting the original down payment and the amount paid over the ten years from the selling price of your house you get $163,554.76. This is more than the principal balance left after ten years. The difference is $16,518.28. This is the amount that you have gained.
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%.
PM T =
P(R/12)
———————
1-(1+R/12)^-12Y
Show work here.
180900(.04735/12)=713.80125
1-(1+.04735/12)^-12×15=0.507791273
713.80125/0.507791273=1405.698144
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_72,125.48___________
Total amount paid_$253,025.48____________
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
163 payments (13yrs. 7 mo.)
Total interest paid over the life of the loan with additional $100 monthly payments______64,712.86_____
Total amount paid with additional $100 monthly payments $245,612.86_______
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?
You would save $7412.62
Part IV: Reflection
Did this project change the way you think about buying a home? Write one paragraph 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.
I already knew that a fifteen year mortgage would save you a lot of money compared to a thirty year. However, it wasn’t until I saw the difference between which payment goes more towards principal than interest that I realized the true proportion of the difference. When the final cost to you figures were tabulated, I was shocked to see the difference in cost! Also, finding out exactly how much you can save by paying a little extra each month was beneficial.
clayboitnott 