# Mortgage Payments

Unit 9 Project: Mortgage Payments The Unit 9 project is an in class project that will be completed over 2 class periods. The final due date for the project is Friday, May 21st, 2021. Each question should be thoughtfully answered with work to support when applicable. Each student will complete their own project but will be allowed to collaborate on the solutions/answers during class time. Please note that collaboration implies equal participation and work from partners, not copying. By the end of the project, you will need to explain your findings in your OWN words. Vocabulary Review: ● Downpayment: The initial payment towards the cost of your house that you pay upfront (not included in your loan). Usually represented in a percentage ● Principal: The total amount of money you owe/borrow ● Interest: The money you pay the lender for the privilege of borrowing money ● Annual Interest Rate: The percentage of the principal that determines the amount of interest you pay each year. You can scale this rate down to the day or month. ○ Example: Annual Interest Rate=2.8% ○ Daily Interest Rate: 2. 8% ÷ 365 = 0. 00767% 𝑝𝑒𝑟 𝑑𝑎𝑦 ○ Monthly interest rate: 0. 00767% × 30 (𝑜𝑟 31) = 0. 2301% 𝑝𝑒𝑟 𝑚𝑜𝑛𝑡ℎ. ● Term of a Loan: Amount of time over which you repay the loan (usually 15 or 30 years) ● Fixed or Variable Rate: fixed rates will stay consistent for the entire term of the loan while variable rates usually start off lower than fixed rates but can change during the term of the loan The following payments are for a 30 year fixed rate mortgage with a 20% downpayment. The total principal, annual interest rate, and original cost of the home is unknown! Month/Year Principal Payment Interest Payment Monthly Payment May 2021 $772.08 $1,197.92 $1,970.00 June 2021 $774.09 $1,195.91 $1,970.00 July 2021 $776.11 $1,193.89 $1,970.00 August 2021 $778.13 $1,191.87 $1,970.00 September 2021 $780.16 $1,189.84 $1,970.00 October 2021 $782.19 $1,187.81 $1,970.00 November 2021 $784.23 $1,185.77 $1,970.00 December 2021 $786.27 $1,183.73 $1,970.00 January 2022 $788.32 $1,181.68 $1,970.00 May 2051 $1,958.97 $11.03 $1,970.00 June 2051 $2,277.98 $5.93 $2,283.91 (last payment is usually slightly larger and does not follow the established pattern) 1. If the data for the mortgage payments above are based on a 30 year fixed rate loan, how many total monthly payments will be made during the entire term of the loan? Answer: 360 2. Does the total monthly payment stay the same or does it change as time goes on? Do the principal and interest payments stay the same or do they change over time? Do the interest and principal payments accurately sum to the correct amount every month? Answer: The total monthly payment stays the same 3. Is the pattern of principal payments a finite or infinite sequence? Why? Answer: finite because the pattern will come to an end. 4. Is the pattern of principal payments arithmetic or geometric? How do you know? Answer: Geometric because it is being multiplied each time. 5. If it is arithmetic, identify the common difference. If it is geometric, identify the common ratio. (please keep at least 4 decimal places in your answer) Show your calculations. Answer: 1.0026 to be 1.0026. Divide the next month by the previous month to find the answer which comes out 6. Based on your observations, what would be the principal payment for February 2022 and March 2022? Show your calculations. Answer: 7. Create an equation to find the nth monthly principal payment. Please use the equation function of google docs to accurately represent your equation (found by going to “insert” and “equation”) Answer: 8. Using your equation, what is your principal payment for the 195th payment? Show your calculations/plugging into your equation. Answer: $1277.72 —————————–STOP HERE AND CHECK IN WITH MS. BRENT———————————— 9. If you have reached this point, you should have realized that the principal payments represent a geometric sequence. What percentage does each principal payment increase by? (Remember, increase and decrease of percentages start at 100% and then go up or down) Answer: 10. Using your answer from #9, if you have the monthly percentage increase, what is the annual interest rate for this mortgage? Answer: 3.12 annual percent rate 11. Create a formula to find the partial sum of the principal payments (Note: the last principal payment is not included in the pattern and therefore should be added in at the end rather than be apart of the equation) Please use the equation function of google docs to accurately represent your equation (found by going to “insert” and “equation”) Answer: 12. Using the total monthly payments from #1 and the fact that the last principal payment is NOT included in the pattern, find the total amount of principal paid during the term of your loan using your equation from #11. Answer: 13. If you paid 20% for your down payment, use the answer to #12 to discover the total cost of your home. How much money did you put down when you purchased the home? Answer: 574,506.83 —————————–STOP HERE AND CHECK IN WITH MS. BRENT———————————–14. Create a formula for the series formed by adding the total monthly payments. Is it arithmetic or geometric? (Note: the last monthly payment is not included in the pattern and therefore should be added in at the end rather than be apart of the equation) Please use the equation function of google docs to accurately represent your equation (found by going to “insert” and “equation”) Answer: 15. Using the total monthly payments from #1 and the fact that the last payment is NOT included in the pattern, find the total amount of money paid during the term of your loan using your equation from #14. Answer: 16. Using your answer from #12 and #15, how much total interest did you pay on this loan over the entire 30 year term? Answer: —————————–STOP HERE AND CHECK IN WITH MS. BRENT———————————–17. Based on your answer to #16, do you think the amount of “extra” money you need to pay in interest for the privilege of borrowing money is a fair amount? What is your opinion? (Remember, this is over a 30 year time period). Answer: 18. Oftentimes, lenders allow for prepayment towards the principal during the term of the loan without any penalties or fees. This means that you are allowed to pay more per month towards your principal than needed. Why might this be beneficial for you? Answer: 19. The loan we analyzed is a fixed rate mortgage meaning the monthly payments are the same every single month with the same interest rate for the entire 30 years. Refinancing is the process of trading in your old mortgage for a new one before it is fully paid off. When you refinance your mortgage, your bank or lender pays off your old mortgage with a new one and then you pay off the new mortgage with new monthly payments. Why might someone want to refinance? Answer: 20. Summarize your findings from the project. a. List out the characteristics of the loan including: original home cost, amount for the down payment, annual interest rate, the term length and the principal owed b. State the connection mortgage payments have to sequences and series. (Make sure to include the type of pattern the principal payments form (and how you know), the meaning behind the common difference/ratio in terms of the loan you chose, the process you took to figure out the original home price, the type of pattern the total monthly payments form (and how you know), and the total amount of interest paid on this loan) Answer:

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