Annuities, Mortgages, and Personal Financehannansg12map4c.weebly.com/uploads/2/6/0/8/26088131/... · Web view[TVM solver/Spreadsheet/Graphing Software - Solve problems using technology

MAP4C. Annuities and Mortgages Assignment. Name_____________ Date________

Annuities, Mortgages, and Personal FinanceActivity 1. Modeling Compound Interest Growth.1. Get a piece of 8.5 inch by 11 inch paper. Get a pen or pencil. 2. Write “6% per year = 0.06” as large as possible on the paper. 3. Fold the paper in half. 4. What time period, or interval of time, does each half represent? 5. Write the interest rate per half interval in decimal form. [Hint: half of 6%?]6. Fold the paper to represent 12 monthly time intervals.7. Write the interest rate per month in each interval.8. Start with $1000. Add the interval interest rate to get the total with interest for each month 1 to 12 using compounding interest. What is the future amount of investing $1000 for 6 monthly intervals, in an account paying 6% per year, compounded monthly? 9. Demonstrate how to model a 2-year investment?


Activity 2. Find the future value of an annuity investment. Goal: Find the future total value of $1000 regularly deposited at the end of each year, into an account paying 10%/a, compounded monthly for 3 years.


Activity 3. Find the total amount of interest paid.

Regular payment: $500 at the end of each year; Interest 12%/year, compounded yearly; Number of payments (N): 3


Personal Finance. Please be aware of the following resources available to you after this course is finished. Write down these web addresses at home. Post them on your fridge for future reference!

Additional Financial Tools are available at:

Financial Consumer Agency of Canada. Website: www.fcac.gc.ca

Canadian Mortgage and Housing Association. Website: www.cmhc.ca

ToolsFormulas

Compound Interest Formula: A = P(1 + i)n

Future Value of an Annuity Formula: FV = Pmt[(1+i)n -1]/i

Present Value of an Annuity Formula: PV = Pmt[1-(1+i)-n]/i

Annuity Payment Formula: Pmt = (Fv)i/[(1+i)n -1] or Pmt = (Pv)i/[1-(1+i)-n]

Where lowercase i represents the compound interval interest rate. Financial institutions state the annual interest rate, but we often need the semi-annual interest rate (annual rate as a decimal / 2) or the monthly interest rate (annual rate as a decimal/12).

Proportional Reasoning and Prerequisite SkillsDid you know?

On our calendar, a leap year occurs when the year is evenly divisible by four, except when the year value is divisible by 400;

Memory aid: The song lyrics “Thirty days hath September; April; June; and November. All the rest have thirty one. Except for February, which has 28, unless it’s a leap year when it has 29.”

Memory aid: Knuckles on your fists also provide a way to remember whether or not a month has 30 days or 31 days. Make two fists and count the knuckle and troughs between the knuckles. Knuckles have 31 days. Troughs between knuckles have fewer days. Do not count the space between your fists as a trough. It memory aid works. Try it!

http://www.cmhc.ca/

http://www.fcac.gc.ca/


Activity 4. Problem Solving Questions Involving Personal Finance.Answer all questions. Use additional paper as required and attach them to this report. You may have to complete some of this work on your own time, using computers, and/or the internet.

1. How many months in each time period? [2 marks]

Years Months5 years10 years20 years25 year30 years

2. How many weeks are in each time period? [2 marks]

Number of Weeks

2 years5 years20 years30 years

3. Depositing $100 per month means depositing how much in each time period? [2 marks]

Amount ($)5 years10 years20 years25 year30


years

4. Earning $40 000 in one year means earning an average of how much in each time period? [3 marks]

Time Period

Amount ($)

a monthone weekone daysix and a half monthsthree months

5. How many payments are made in one year for each payment frequency? [3 marks]

Frequency

Number of payments per year.

Monthlyquarterlysemi-annuallyWeeklybi-weeklysemi-monthly

6. State whether or not the year shown is a leap year. [3 marks]

a) Year 2012? Explain how we know.

b) Year 2013? Explain how we know.


c) The year that will you turn age 65 is______. Is it a leap year? How do you know?

7. Calculate the value of the following exponential expressions: [3 marks]

a) 1000(1.0325)1

=

b) 1000(1.0325)60

=

c) 1000(1.0325)-60

8. a) State the compound interest formula in terms of A, P, i, and n. ______________ b) Rewrite the compound interest formula A=P(1+i)n in terms of FV, PV, i, and n.

[2 marks]

9. True or False? Multiplying a value by one will result in a larger value. Give an example. [1 mark]

10. True or False? Multiplying any positive number by a number greater than one will result in a larger value. [1 mark]

11. True or False? Multiplying any positive value by a number between zero and one will result in a larger value. [1 mark]

12. True or False? The number 0.804 is greater than the number 0.84. [1 mark]

13. True or False? The number “1 + an increase of 5%” is greater than one. [1 mark]

MAP4C. Annuities and Mortgages Assignment. Name_____________ Date________14. True or False? A 5% decrease in value can be found by multiplying the initial value by 0.95. [1 mark]

15. True or False. A 5% increase in value can be found by multiplying the initial value by 1.05. [1 mark]

16. True or False. Another way of saying “per year” is “per annum”. [1 mark]

17. True or False. Another way of writing “per annum” is “/a”. For example, “6%/a”. [1 mark]

18. True or False. A series of payments or deposits paid at regular intervals is called an annuity. [1 mark]

19. True of False. Understanding math improves the likelihood of making good financial decisions. Justify the statement. [1 mark]

20. True or False. The interest rate per compounding interval is often represented as the variable “i”. [1 mark]

21. True or False. The compound interest formula A=P(1+i)n can also be written as the future value formula FV = PV(1+i)n. [1 mark]

22. How is an annuity different from a one-time investment? Show the difference visually using time lines. [2 marks]


23. Show step-by-step how the future value formula, FV = PV(1+i)n, can be rearranged to give us the present value formula PV = FV(1+i)-n. [2 marks]

24. How many semi-monthly payments will be made if payments are made for a period of one year? Explain your reasoning. [1 mark]

25. How many bi-weekly payments will be made if payments are made for a period of one year? Explain your reasoning. [1 mark]

26. Solve 8000 = 1.005n. Do not round. Hint: Use log button. [2 marks]

27. Solve 9000 = X60. Do not round. [2 marks]

28. Solve 7000 = (1+i)60. Do not round. Show all steps. [2 marks]


29. Write is radical form, then evaluate:8134 . [1 mark]

30. True or False. A mortgage is a type of annuity. [1 mark]

31. Show the calculations. A person buys a home for $300 000 on June 1st, 2016. The home value increases 3% each year. What is the value of the home at each of these times in the future? :

a) June 2017?

b) June 2018?

c) June 2026? [3 marks]

32. What is meant by home equity? Give a numeric example to support your explanation. [2 marks]

33. You are buying a $300 000 property and make a down payment of 5% of its value. [5 marks]

a) Show how to calculate the amount of the down payment.

b) Show how to calculate the amount of money needed for the mortgage.

c) How much equity would you have in the property on the date purchased?


d) Assume the property increase in value by 2.5% yearly, calculate the value of the property each year for the next 5 years. Use a data table with appropriate column titles to display the information.

34. Determine the future value of a single investment of $1000 at 4% per year, compounded annually, for 45 years. [5 marks]

35. Draw a time line diagram to represent an annuity situation where $200 per month is invested into an account for six months, at an annual interest rate of 4%. Calculate the future value of the annuity. [5 marks]

MAP4C. Annuities and Mortgages Assignment. Name_____________ Date________36. Research, gather and interpret information about common real-life annuities such as RRSPs, RESPs, and RRIFs, describe the key features of an annuity. [6 marks]

Annuity Key Purpose/FeaturesRRSP What does this mean?

How does it work?

RESP What does this mean?

How does it work?

RRIF What does this mean?

How does it work?

MAP4C. Annuities and Mortgages Assignment. Name_____________ Date________37. Use a TVM calculator (see teacher). In the table below, write the meaning of each of the variables represented in the Time-Value-of-Money app: [no marks]

N= Number of paymentsI%= Annual interest ratePV= Present ValuePMT= Regular PaymentFV= Future ValueP/Y= Number of payments per yearC/Y= Number of compounding intervals per

yearPMT:END BEGIN

<Are payments made at the end or beginning?>

38. Given an ordinary simple annuity with semi-annual deposits of $1000, earning 6% interest per year compounded semi-annually, over a 20-year term, show which of the following results in the greatest return by drawing the TVM app data table contents for each situation and writing a summary conclusion:Doubling PaymentN=I%=PV=PMT= -

2000

FV=P/Y=C/Y=PMT:END BEGIN

Double payments to $2000?

N=I%= 12PV=PMT=FV=P/Y=C/Y=PMT:END BEGIN

Doubling the Interest Rate?

N=I%=PV=PMT=FV=P/Y= 4C/Y=PMT:END BEGIN

Doubling the frequency of the payments and also doubling the compounding frequency?

N=I%=PV=PMT=FV=P/Y=C/Y=PMT:END BEGIN

Doubling the payment amount and compounding frequency to four times each year?

Conclusion: [20 marks]

MAP4C. Annuities and Mortgages Assignment. Name_____________ Date________39. [TVM solver/Spreadsheet/Graphing Software - Solve problems using technology that involve the amount, the present value, and the regular payment of an ordinary simple annuity.] Task: Show how to calculate the total interest paid over the life of a $10 000 loan with monthly repayments over 2 years at 8% per year compounded monthly, and compare the total interest with the original principal of the loan. Does it surprise you how much interest must be repaid? Of the total amount paid, what amount and percent is principal and what amount and percent is interest? Draw a stacked bar graph to visually display these percentages. [10 marks]

MAP4C. Annuities and Mortgages Assignment. Name_____________ Date________40. [Curriculum: Demonstrate an understanding of annuities used as long-term savings plans.] a) What is an annuity? [2 marks]

b) Problem: Using the annuity formula, Pmt= (FV ) (i )((1+i )n−1 ) , show how to calculate

the monthly payment required to save $20000 over 5 years, in a savings account at 2.5%/a, compounded monthly.

[8 marks]

MAP4C. Annuities and Mortgages Assignment. Name_____________ Date________41. [Curriculum: demonstrate, through investigation using technology (e.g., a TVM Solver), the advantages of starting deposits earlier when investing in annuities used as long-term savings plans.] Problem: If you want to have a million dollars at age 65, how much would you have to contribute monthly into an investment that pays 6% per annum, compounded monthly, beginning at age 20? At age 35? At age 50? Show your work. Write to explain your reasoning. [10 marks]

Starting Age 20 Starting Age 35 Starting Age 50

42. [gather and interpret information about mortgages, describe features associated with mortgages (e.g., mortgages are annuities for which the present value is the amount borrowed to purchase a home; the interest on a mortgage is compounded semi-annually but often paid monthly), and compare different types of mortgages (e.g., open mortgage, closed mortgage, variable-rate mortgage)]. Tasks: [5 marks]

a) Explain the difference between an open mortgage and a closed mortgage.

b) Explain the difference between a variable-rate mortgage and a fixed rate mortgage, using an example.


c) State the compounding frequency used to calculate Canadian mortgages. 43. [Curriculum: Read and interpret an amortization table for a mortgage] Task: You purchase a condominium with a $25 000 down payment, and you mortgage the balance at 6.5% per year, compounded semi-annually, over 25 years, payable monthly. Use an amortization table to compare the interest paid in the first year of the mortgage with the interest paid in the 25th year. Use a 5-year term. [10 marks]

a) How much money was borrowed to purchase the house? _______________

b) What was the purchase price of the house?........................_______________

c) How often must payments be made?................................ _______________

d) How much money must be paid each month?................... _______________


e) How much principal was paid in month 1? _____ month 12?________f) How much interest was paid in month 1?_____ ; month 12?________g) If, one year after the date of purchase, the house increase in value 3%,

determine the change in house value, and in net worth, due to owning the house.

[10 marks]44. [Curriculum: Generate an amortization table for a mortgage, using a variety of tools and strategies (e.g., input data into an online mortgage calculator; determine the payments using the TVM Solver on a graphing calculator and generate the amortization table using a spreadsheet), calculate the total interest paid over the life of a mortgage, and compare the total interest with the original principal of the mortgage.] Task: Use the Government of Canada online mortgage calculator available at www.fcac.gc.ca to create a mortgage payment schedule for a Canadian mortgage amount between $150 000 and $350 000 at 5%/a, amortized for 25 years. Use a 5-year term. List the results of the amortization summary table (show variable names and values). [10 marks]


MAP4C. Annuities and Mortgages Assignment. Name_____________ Date________45. [Curriculum: Making comparisons between mortgage options. Determine, through investigation using technology (e.g., TVM Solver, online tools, or financial software), the effects of varying payment periods, regular payments, and interest rates on the length of time needed to pay off a mortgage and on the total interest paid.] Task: Create and print mortgage schedules using the mortgage tools available at www.fcac.gc.ca , then use these reports to calculate the interest saved on a $100 000 Canadian (compounded semi-annually) mortgage with monthly payments, at 6% per annum, when it is amortized over 20 years instead of 25 years. Clearly state your findings for each. Use a 5-year term.

[10 marks]

20 year Amortization vs. 25 year Amortization


MAP4C. Annuities and Mortgages Assignment. Name_____________ Date________46. . Research a town-home, or single detached hope, for sale in Durham Region. Can a couple afford the home on a family income of $50 000 per year? $90 000 per year? Report on your Investigation. Explain your reasoning. Provide mathematical evidence to support your reasoning.

Online, find a home for sale in the range of $200000 to $400000; Start a Word document file to write a report; Determine the down payment amount at 10% of the home

price:_______________; Determine the amount of the mortgage required:_____________________; Determine the monthly payment required: _________________; Write a monthly budget showing income, expenses, and balance

remaining. Include $1200 for food; monthly mortgage payment amount; utilities at $400/mo.; phone at $80/mo; clothing at $100/mo.; entertainment at $100/mo.; maintenance at $100/mo.; transportation at $200/mo.; plus any other items that you care to include.

Submit a report summarizing your findings. Can this couple financial afford such a home on their income? JUSTIFY your conclusions.

Q46. Marking Rubric Level 1(50-59) 5

Level 2(60-69) 6

Level 3(70-79) 7[Meets Provincial Standard]

Level 4(80 – 100) 8 9 10

Thinking and Inquiry. Ability to comprehend the situation and find information.

Little evidence provided. Substantially below standard expected.

Some evidence provide, but lacks detail.

Sufficient inquiry evidence provided.

Thoroughly researched and documented. Student clearly understands the scope of the assignment.

Application of mathematical reasoning.(Down payment issues addressed.)(Payment schedule showing monthly principal, interest, and balance owing is included).(Other monthly financial issues addressed food, etc.)

Little, or incorrect, mathematical reasoning is evident.

Some mathematical reasoning is evident; Reasoning may contain some small or non-significant errors.

Good mathematical reasoning clearly evident.

Thorough mathematical reasoning is evident and referenced in the report.

Communication:(Report is clearly written and effectively communicated with proper spelling

Little or no written statements or

Some written statements to support or evidence

Substantial written statements or evidence

Thorough written statements and evidence clearly support the financial argument.

MAP4C. Annuities and Mortgages Assignment. Name_____________ Date________, punctuation, and grammar; Report includes: a photo of the home for sale ad; an fcac.gc.ca mortgage payment schedule; a viable 12-month budget; and a written explanation and summary.

evidence to support the financial argument.

to support the financial argument.

to support the financial argument.

Total (out of 30)

Documents

Annuities, Mortgages, and Personal Financehannansg12map4c.weebly.com/uploads/2/6/0/8/26088131/... · Web view[TVM solver/Spreadsheet/Graphing Software - Solve problems using technology