This course continues to explore, in greater depth, standard algebra topics many of which were addressed in Math 1010. Topics include the following: functions, including polynomial, rational, exponential, and logarithmic; systems of equations; matrices and determinants; partial fraction decomposition; conics and sequences and series.
Mortgage Project
Introduction
In this project we will examine a home loan or mortgage. Assume that you have found a home for sale 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
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). 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. (Free amortization spreadsheet on the web: bretwhissel.net/amortization/)
Amortization Schedule monthly payment for a 30 year mortgage = $968.35 Total interest paid over 30 years = $167,704.53 Total amount paid = $348,604.53
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?
The more payments you make the amount of the payment that goes towards the principal goes up while the amount that is going towards interest goes down.
Number of first payment when more of payment goes toward principal than interest: Payment 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 state above?
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 down, 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 and losses: Selling price of your house = $299,856.76 Original down payment = $20,100 Mortgage paid over the ten years = $116,202 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:
$299,856.76 - $147,036.48 = $152,820.28 (How much was made out of selling the house) $152,820.28 - $116,202 = $36,618.28 (How much you came out ahead, after paying off loan) If you made $299,856.76 from selling the house then paid off the remainder of the loan, $147,036.48 you have $152,820.28 left over. If you take how much you put into the house ($116,202) from how much you made from it you learn that you gained $36,618.28 from selling.
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 berates cent). For the 15 year loan use an annual interest rate of 4.735%
Monthly Payment for a 15 year mortgage = $1,405.70
Use the amortization spreadsheet on the web again, (bretwhissel.net/amortization/) this time entering the interest rate and number of payments for a 15 year loan. Amortization Schedule monty payment for a 15 year mortgage = $1,405.70 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 = 5th payment
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? Length of time to pay off loan with additional payments of $100 per month = 13.58 years or 163 payments Total interest paid over the life of the loan with additional $100 monthly payments = $64,713.29 Total amount paid with additional $100 monthly payments = $245,613.29
Compare this toal 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?
$253,026 - $245,613.29 = $7,412.71 You would save $7,412.71 more if you just paid $100 extra towards your principal payment each month.
Part IV: Reflection
This project really did change my outlook on home buying. I have never truly understood how all the payments and things worked, it was good to have each payment plan laid out in front o you payment by payment on the amortization spreadsheet. Using the spreadsheet really helped me visually to understand how paying off a home loan works. I always thought that just paying a simple $100 a month extra towards your house payment wouldn't do much because $100 compared to the $200,000 or more you paid towards the ouse doesn't seem like a lot. I didn't realize that paying over the monthly payment all goes towards the loan without interest taken out on it. I know when I buy my first home that I will pay as much as my budget allows me to pay extra on my house payment. To me it seems easier to pay a little extra to pay off the house sooner instead of just paying the monthly amount and having to pay on it or longer, it is better to suffer for a little bit rather than a longer period of time in my eyes.