Accelerated PreCalculus/Trig 3
Name: ____________________________________
Annuity Project - Mortgages
Due Date: ________________________________
Welcome to the real world. In this project, you will be getting a job, earning a yearly salary, and buying a house in
Pennsylvania, New Jersey, Delaware, or New York.
First start by finding a job that you are interested in from the Bureau of Labor Statistics website (http://www.bls.gov/oco/) and looking
up the average salary and education needed to obtain that degree.
Career:
______
Salary: $____________________________
Marital: Single
Education (circle one):
High School Diploma
Associates
Ph.D. (non-med)
Bachelor
Masters
Law Degree
Ph.D. (medical)
Calculate the following expenses you have before looking for a house to buy. This list of expenses will help you determine how
much you can afford to spend on a house. Round all decimals to the nearest hundredth.
INCOME:
1. Annual income (Salary from above)
_________________________ 1
2. Monthly income (Line 1 divided by 12)
_________________________ 2
FEDERAL TAX CALCULATION:
3. Yearly contribution to your 401K/403B/IRA (Line 1 times .07 )
_________________________ 3
4. IRS personal exemption amount
_______$3950.00___________ 4
5. IRS Standard deduction for a single person
_______$6200.00___________ 5
6. Yearly medical insurance premiums
_______$2000.00___________ 6
7. Sum of Lines 3 through 6
_________________________ 7
8. Line 1 minus Line 7 (This represents your Federal Taxable Income)
_________________________ 8
9. Amount of yearly Federal Tax (Determine using Line 8 and the Tax Table provided)
_________________________ 9
If Taxable Income is…
Not over $9,075
Over $9,075 but not over $36,900
Over $36,900 but not over $89,350
Over $89,350 but not over $186,350
Over $186,350 but not over $405,100
Over $405,100 but not over $406,750
Over $406,750
The Tax Is…..
10% of the taxable income
$907.50 + 15% of the amount over $9,075
$5,081.25 + 25% of the amount over $36,900
$18,193.75 + 28% of the amount over $89,350
$45,353.75 + 33% of the amount over $186,350
$117,541.25 + 35% of the amount over $405,100
$118,188.75 + 39.6% of the amount over $406,750
MONTHLY TAXES:
10. Monthly Federal Tax (Line 9 divided by 12)
_________________________ 10
11. Monthly PA Tax (Line 2 times .0307)
_________________________ 11
12. Monthly Local/Municipality Tax (Line 2 times .01)
_________________________ 12
13. Monthly Social Security contribution (Line 2 times .062)
_________________________ 13
14. Monthly Medicare contribution (Line 2 times .0145)
_________________________ 14
15. Monthly Unemployment Tax (Line 2 times .0007)
_________________________ 15
16. Sum of Lines 10 through 15 (This represents the total amount you spend in taxes each month) __________________________ 16
NECESSARY MONTHLY EXPENSES:
17. TV, Internet, Phone
_________________________ 17
18. Food (Groceries)
_________________________ 18
19. Gas for car
_________________________ 19
20. Water and sewer bill
________$50.00____________ 20
21. Heating (natural gas, propane, oil, electric, hot water?)
________$60.00____________ 21
22. Electric bill (Air conditioning, hot water?)
________$90.00____________ 22
23. Student loan payments (find your monthly payment below and write in line 23)
College Loan Payments – Depending on your level of college education, you have a
different amount you owe in student loans. See below for your options:
• Associate’s Degree: You owe $3,500 in college debt and pay $100 per month
• Bachelor’s Degree: You owe $10,000 in college debt and pay $250 per month
• Master’s Degree: You owe $15,000 in college debt and pay $275 per month
• Law Degree: You owe $108,293 in law school debt and pay $650 per month
• Ph.D. (non-med): You owe $15,000 in college debt ad pay $250 per month
• Ph.D. (medical): You owe $125,456 in medical school debt and pay $850 per month
_________________________ 23
24. Medical/Dental plan premiums (Line 6 divided by 12)
_________________________ 24
25. 401K/403B/IRA contribution (Line 3 divided by 12)
_________________________ 25
26. Car insurance
_______$100.00____________ 26
27. Miscellaneous expenses (entertainment, dining out, clothing)
_________________________ 27
28. Sum of Lines 17 through 27
_________________________ 28
29. Amount left to spend on mortgage/housing (Line 2 minus Line 16 minus Line 28)
_________________________ 29
Congratulations! You are now ready to buy a home.
30. Find a home in the area to buy (Pennsylvania, New Jersey, Delaware, or New York).
 The cost of the house must be between $100,000 and $1,000,000.
 Recommended websites: www.realtor.com, www.realestate.com, www.trulia.com, www.everyhome.com, www.zillow.com
 Print out the website with your housing information – you will need to turn this website in for credit.
 Write the cost of the house on line 30.
_________________________ 30
31. You are putting a 10% down payment on the house.
Determine the amount of the down payment. (line 30 times .1)
_________________________ 31
32. Determine the amount of your house that needs to be financed/mortgaged (your loan).
(line 30 minus line 31)
_________________________ 32
DETERMING WHAT TYPE OF MORTGAGE YOU SHOULD CHOOSE:
FINDING THE MONTHLY PAYMENT OF YOUR MORTGAGE/LOAN:
Use the following Present Value of an Annuity formula for #33-35 to find “p”:
𝑃𝑛 = 𝑝 [
1−(1+𝑖 )−𝑛
𝑖
]
𝑃𝑛 = 𝑃𝑟𝑒𝑠𝑒𝑛𝑡 𝑉𝑎𝑙𝑢𝑒 𝑜𝑓 𝑎𝑛 𝐴𝑛𝑛𝑢𝑖𝑡𝑦 (𝑙𝑜𝑎𝑛)
𝑝 = 𝑟𝑒𝑝𝑒𝑎𝑡𝑒𝑑 𝑝𝑎𝑦𝑚𝑒𝑛𝑡 (𝑚𝑜𝑛𝑡ℎ𝑙𝑦 𝑙𝑜𝑎𝑛 𝑝𝑎𝑦𝑚𝑒𝑛𝑡)
𝑖 = 𝑖𝑛𝑡𝑒𝑟𝑒𝑠𝑡 𝑟𝑎𝑡𝑒 ÷ # 𝑜𝑓 𝑝𝑎𝑦𝑚𝑒𝑛𝑡𝑠 𝑝𝑒𝑟 𝑦𝑒𝑎𝑟 (12 𝑖𝑓 𝑝𝑎𝑦𝑖𝑛𝑔 𝑚𝑜𝑛𝑡ℎ𝑙𝑦)
𝑛 = # 𝑜𝑓 𝑝𝑎𝑦𝑚𝑒𝑛𝑡𝑠 𝑜𝑣𝑒𝑟 𝑡ℎ𝑒 𝑙𝑖𝑓𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑙𝑜𝑎𝑛 (12 𝑝𝑎𝑦𝑚𝑒𝑛𝑡𝑠 𝑎 𝑦𝑒𝑎𝑟 × # 𝑜𝑓 𝑦𝑒𝑎𝑟𝑠)
33. Structure 1: Find your monthly loan payment (p) for paying off your house in 30 years:
 If your loan/mortgage is between $0 – $417,000, your interest rate is 4.250% (.0425)
 If your loan/mortgage is between $417,000 – 1,000,000, your interest rate is 4.375% (.04375)
𝑃𝑛 = (𝑙𝑖𝑛𝑒 32) = ________________________________
𝑖 = ________________________________
𝑛 = ________________________________
𝑀𝑜𝑛𝑡ℎ𝑙𝑦 𝑙𝑜𝑎𝑛 𝑝𝑎𝑦𝑚𝑒𝑛𝑡 = 𝑝 = ________________________________

What is the total amount that you paid for your house in the end? _________________________

What is the total amount of interest that you paid during the life of the loan? _________________________
34. Structure 2: Find your monthly loan payment (p) for paying off your house in 20 years:
 If your loan/mortgage is between $0 – $417,000, your interest rate is 4.125% (.04125)
 If your loan/mortgage is between $417,000 – 1,000,000, your interest rate is 4.25% (.0425)
𝑃𝑛 = (𝑙𝑖𝑛𝑒 32) = ________________________________
𝑖 = ________________________________
𝑛 = ________________________________
𝑀𝑜𝑛𝑡ℎ𝑙𝑦 𝑙𝑜𝑎𝑛 𝑝𝑎𝑦𝑚𝑒𝑛𝑡 = 𝑝 = ________________________________

What is the total amount that you paid for your house in the end? _________________________

What is the total amount of interest that you paid during the life of the loan? _________________________
35. Structure 3: Find your monthly loan payment (p) for paying off your house in 15 years:
 If your loan/mortgage is between $0 – $417,000, your interest rate is 3.375% (.03375)
 If your loan/mortgage is between $417,000 – 1,000,000, your interest rate is 3.5% (.035)
𝑃𝑛 = (𝑙𝑖𝑛𝑒 32) = ________________________________
𝑖 = ________________________________
𝑛 = ________________________________
𝑀𝑜𝑛𝑡ℎ𝑙𝑦 𝑙𝑜𝑎𝑛 𝑝𝑎𝑦𝑚𝑒𝑛𝑡 = 𝑝 = ________________________________

What is the total amount that you paid for your house in the end? _________________________

What is the total amount of interest that you paid during the life of the loan? _________________________
In addition to your monthly loan payment, you must also pay the following:
MONTHLY MORTGAGE/HOUSING EXPENSES:
36. Property taxes (school, county, municipality: this should be listed on the housing website)
Yearly amount $_____________ divided by 12
_________________________ 36
37. Hazard/property (homeowner’s) insurance
______$60.00______________ 37
38. Homeowner’s association dues (HOA), if applicable (see website)
_________________________ 38
39. Private Mortgage Insurance (PMI): (Line 32 times .0055 divided by 12)
(this is to protect the bank from losing money on an unexpected foreclosure)
_________________________ 39
TOTALING YOUR MONTHLY HOUSING COSTS:
40. Structure 1 (If you were to pay off your mortgage in 30 years):
(Sum of Lines 36 – 39 and “p” from line 33)
_________________________ 40
41. Structure 2 (If you were to pay off your mortgage in 20 years):
(Sum of Lines 36 – 39 and “p” from line 34)
_________________________ 41
42. Structure 3 (If you were to pay off your mortgage in 15 years):
(Sum of Lines 36 – 39 and “p” from line 35)
_________________________ 42
HOW MUCH EXTRA MONEY YOU’D HAVE TO SPEND EACH MONTH:
43. Structure 1 (If you were to pay off your mortgage in 30 years):
(Line 29 minus Line 40)
_________________________ 43
44. Structure 2 (If you were to pay off your mortgage in 20 years):
(Line 29 minus Line 41)
_________________________ 44
45. Structure 3 (If you were to pay off your mortgage in 15 years):
(Line 29 minus Line 42)
_________________________ 45
ANALYSIS QUESTIONS:
Please type your answers to the following questions and staple them to your packet.
1. Compare the three mortgage structures. In terms of its monthly payment, which mortgage structure would be the least
expensive?
2. Compare the three mortgage structures. In terms of the amount paid in interest, which mortgage structure would be the least
expensive?
3. Compare the three mortgage structures. In terms of total amount paid for the home, which mortgage structure would be the
least expensive?
4. Which mortgage structure is best suited for you and why? This question is an extension for the project. You should consider
a future plan when answering this question…What will your career be? What will your budget look like? How large of a
family will you have? Based on at least these considerations, decide which mortgage structure would be the best for you and
why. You may also come to the conclusion that this house is not realistic for you based on your future plans. Note: This
question is worth 5 points out of the total 50. Basic answers such as: “I would choose Structure -- because it is the
cheapest.” will receive minimal points. This question is an opportunity for you to be creative and go above and beyond. I
want to see genuine thought and analysis. Earning a 5/5 requires going above and beyond.
Grading Checklist: This project will be worth a total of 50 points in the SUMMATIVE ASSESSMENT category of your first
marking period grade. (In other words, it counts as a quiz).
Item
Points Earned
Points Possible
Job
2
House Information
5
Calculations
7
Structure 1
5
Structure 2
5
Structure 3
5
Content of Questions #1-3
5
Content and Analysis of Question #4
5
Grammar, Spelling, Mechanics, etc.
3
Overall Neatness, Professionalism, Creativity, and Organization
3
Use of Class Time
5