Math 1090 Mortgage Project
Amie Bergstrom
4/16/2013
Let say I purchased a home for the price of $201,000.00, and I have a down payment of 20,100.00 dollars. That would be 10% down on the home. The amount that the loan will be financed for will be 180,900.00. My mortgage is a 30 year loan. To figure out what my payment will be on a 30 year loan I will use the amortization schedule formula. If my numbers are accurate my monthly payment will be $968.35 for interest and principle only. This does not include insurance or taxes for the home.
Over a 30 year period I will end up paying 167,706 in interested. The total amount paid for the home with interested and principal will be 348,606 if I make the same monthly payment every month. The more payments I make on the home the more the payment will go towards principal. After I have made 194 payments then more money will go to the actual principal. I also want to make sure I have enough money for other things like, home insurance, property taxes as well as money for utilities, food and entertainment. I have decided that my monthly principal and interested payment should not go over 35% of my monthly take home pay. To figure out what 35% of my minimum take home pay should be, I will divide my monthly payment by 35%. I should have a minimum monthly take home pay of $2766.71. My take home pay after taxes is less than my gross pay. My net pay is 73% of my gross pay. My minimum gross annual salary will need to be $45480.12. I figured out this number by taking my take home pay and dividing it by 73%, which gave me gross monthly income of $3790.01. I then needed to times that number by 12 to come up with the annual salary.
After I have lived in the house for 10 years I will want to sell the home. As long as the economy is doing well, the house value should increase over 10 years. I will find the value of the home after 10 years by taking a continuous interest rate of 4%. Using the continuous compound interest formula, I have found the value of my home after 10 years will be worth $299856.76. If I add the amount I put down on the home when I first bought it of 20100, the mortgage paid over 10 years would be 33, 86.52 and the principal balance on my loan would be $147036.48. I have actually gained $98.856.76 in equity.
Let see the difference if I were to finance a 15 year mortgage instead of a 30 year mortgage. Again I will use the amortized schedule formula. My calculations show that my monthly payment for a 15 year mortgage would be 1405.70. Total interest paid over 15 years would be 72,126.00 and total amount paid would be 253,026.00. I would only have to make 5 payments before more of the payment goes towards interest than principal and it would take me 1358 years to pay off the loan if I made $100.00 more toward the payment a month. Also, if I paid $100.00 dollars more a month my total amount of interest paid over the life of the loan would be $64713.29 and the total amount of the home paid would be 245,613.29.
This project did not make me think different about buying a home. I have purchased two homes already and have gone through the process. It is interesting to see how much faster your loan will be paid off when you make an extra payment towards the loan amount every month. You can also shorten your interest amount by paying biweekly instead of monthly. I also learned how to come up with the numbers on my own so I can figure out the payments for myself rather than by what the mortgage company tells me. I feel great now that I know how to do the calculations on my own rather than using a program. This project was a great project to really put math in play to the real world and see how useful it really can be.
