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Toward Quantitative Literacy: Interesting Problems in Finance

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  • 1. Toward Quantitative Literacy: Interesting Problems in Finance Jim Ham http:// www.delta.edu/jaham 2008 AMATYC Conference Washington, D.C. Saturday, November 22, 2008
  • 2.
    • Pick up a graphing calculator.
    • Complete page 1 of the handout by filling in the blanks.
    Toward Quantitative Literacy: Interesting Problems in Finance Jim Ham http:// www.delta.edu/jaham 2008 AMATYC Conference Washington, D.C. Saturday, November 22, 2008
  • 3.
    • 51 % of workers age 55 and up have saved less than $50,000 for retirement (not including the value of a primary residence).
    • The average household has a net worth of just $264,000 at retirement, not including home equity.
    • The savings rate for all of 2006 was -1% .
    • 50% of all retirement plan participants who change jobs fail to roll over their accounts.
    • People in the 18 to 24 age bracket spend nearly 30% of their monthly income just on debt repayment.
    • Only about 1 in 20 American households owes $8,000 or more on credit cards.
    • 55% of Americans owe nothing on their credit cards.
    • More than 1% of all U.S. households were in some phase of the foreclosure process last year.
    • More than 75% of undergraduates began the 2004 school year with credit cards.
    • 24% of undergraduates use their credit cards for tuition. The average student credit card balance is $2,347 .
    • In 2005, students in a survey believed when they got older that they would earn an average salary of $145,000 . In 2005, adults with a bachelor's degree earned an average of $54,689 .
    • 26% of teens and young adults say their parents taught them how to manage money.
    • 15% of high school graduates nationally have taken a course covering personal finance content.
    • The average 30-year fixed mortgage rate is approximately 6% .
    • Subprime mortgages charge an interest rate lower than the prime lending rate in the first couple of years, but the rate goes up rather dramatically after a period of two to three years. False .
    • Each time you open a store credit card, 20 points are taken off of your credit score.
    • In the first quarter of 2008, home values decreased by 7.7% .
  • 4.  
  • 5.
    • 51 % of workers age 55 and up have saved less than $50,000 for retirement (not including the value of a primary residence).
    • The average household has a net worth of just $264,000 at retirement, not including home equity.
    • The savings rate for all of 2006 was -1% .
    • Only 11% of workers under 35 years of age indicate they are participating in their company's 401(k). (American Institute of Certified Public Accountants) 50% of all retirement plan participants who change jobs fail to roll over their accounts.
  • 6.  
  • 7.
    • 62% of college graduates will have a student loan debt averaging $27,236 (Student Monitor)
  • 8.  
  • 9.
    • People in the 18 to 24 age bracket spend nearly 30% of their monthly income just on debt repayment.
    • The average household credit card debt is about $8000.
    • Only about 1 in 20 American households owes $8,000 or more on credit cards.
    • 55% of Americans owe nothing on their credit cards.
  • 10.  
  • 11.
    • 26% of teens and young adults say their parents taught them how to manage money.
    • In most cases, economics and personal financial literacy programs are elective classes so “only 15% of Americans graduate from high school having learned anything about money at all.”
    • Research shows that individuals that have taken personal finance education course have a higher savings rate, higher net worth and make larger contributions to their 401k. (The Department of the Treasury)
  • 12.
    • Students do not take courses in personal finance
      • Saving & Investing
      • Debt Management
      • Budgeting
    • Here’s where we come in ….
      • Integrate financial applications in our classes
  • 13.
    • The problems in your handout
      • A 3-week unit in “Finite Mathematics”
      • Proposed for a Liberal Arts Math Course
      • Individual problems used in lower level courses
      • Many, but not all, use the TVM Solver of the graphing calculator.
  • 14.
    • The Compound Interest Formula
    • What mathematical skills do students employ when using this formula to solve problems?
  • 15.
    • The TVM (Time Value of Money) Solver
    • N = Number of Payment Periods ( N = mt)
    • I% = Annual Interest Rate Do not convert the APR to a decimal. If APR = 9.5%, then I% = 9.5.
    • PV = Present Value Amount of a loan or beginning lump sum investment. Enter Cash Inflows as positive values and Cash Outflows as negative values.
    • PMT = Periodic Payment (or Deposit) The payment is usually a Cash Outflow, and hence, a negative value.
    • FV = Future Value
    • P/Y = Payments Periods per Year
    • C/Y = Compounding Periods per Year C/Y is automatically set to match P/Y. If C/Y is different from P/Y, enter P/Y first, then C/Y.
  • 16.
    • The TVM (Time Value of Money) Solver
    • PMT: END BEGIN (When the regular payments are made: at the BEGINing of the period or at the END) PMT: END is used for an ordinary annuity, where payments occur at the end of each payment period. Most loans are in this category. PMT: BEGIN is used for an annuity due, where payments occur at the beginning of each payment period. Most leases are in this category.
    • To get to the TMV Solver on the TI-84, enter APPS, Finance, TVM Solver.
    • While the cursor is blinking on the value to be calculated, enter ALPHA ENTER (SOLVE).
  • 17. Problem 1: Lump Sum Investment: When Bud Uronner was born, his grandfather made an initial deposit of $3,000 into an account for his college education. Assuming an interest rate of 6% compounded quarterly, how much will the account be worth in 18 years?
  • 18. $8,833.25 365 $8,828.54 52 $8,810.30 12 $8,763.47 4 $8,694.83 2 $8,563.02 1 A (r = .06; P = 3000; t = 18) m
  • 19. $100,635.40 .20 $30,005.83 .13 $14,889.50 .09 $12,483.42 .08 $7,337.76 .05 $3,590.85 .01 A (m = 4; P = 3000; t = 18) r
  • 20. Problem 2: Rule of 72: Orson Buggy wants his $5,000 investment to double in 6 years. What annual interest rate must he earn? Assume interest is compounded annually.
  • 21. 69.9863 1.9441 36 70.3254 2.9302 24 70.6666 3.9259 18 71.3557 5.9463 12 72.0538 8.0060 9 72.4062 9.0508 8 73.4772 12.2462 6 75.6828 18.9207 4 77.9763 25.9921 3 82.8427 41.4214 2 r * t r t
  • 22. Problem 4: Future Value Annuity: How long will it take Dot Snice to accumulate $1,000,000 if she invests $3,000 per year at an annual interest rate of 8%? Assume interest is compounded annually.
  • 23. 23.12 .20 31.02 .13 39.85 .09 43.14 .08 58.86 .05 147.37 .01 t (m = 1; R = 3000; S = 1000000) r
  • 24. Problem 7: Present Value Annuity – Monthly Payment: Megan Model borrows $25,000 at 7.53% compounded monthly. If she wishes to pay off the loan after 15 years, how much would the monthly payment be?
  • 25. $853.29 30 $911.53 25 $1,006.52 20 $1,132.75 16 $1,175.99 15 $1,532.90 10 R (m = 12; r = .065; S = 135000) t
  • 26.
    • Problem 6a: Invest Early and Often
    • Much has been written about the importance of investing early and often. Two friends saved for retirement over a 40-year period in two different ways. Johnny on the Spot invested $4,000 per year at 8% annual interest for the first twenty years, then invested nothing over the last 20 years. During the last 20 years, his investments accumulated interest at 9% annual interest. Johnny Come Lately invested nothing for the first twenty years, but then invested $10,000 per year over the next 20 years at 9% annual interest.
    • How much did Johnny on the Spot invest over the 40-year period?
    • How much did Johnny Come Lately invest over the 40-year period?
    • How much did Johnny on the Spot accumulate over the 40-year period?
    • How much did Johnny Come Lately accumulate over the 40-year period?
    • Who was the wiser investor and why?
  • 27.
      • Problem 6a:
      • How much did Johnny on the Spot invest over the 40-year period? $80,000
      • How much did Johnny Come Lately invest over the 40-year period? $200,000
      • How much did Johnny on the Spot accumulate over the 40-year period? $1,025,875.40; $183,047.86 after the first 20 years.
      • How much did Johnny Come Lately accumulate over the 40-year period? $511,601.20
      • Who was the wiser investor and why? Johnny on the Spot. He invested less than half the money, yet earned about twice as much or a half million dollars more.
    N= 20 I%= 9 PV= -183047.86 PMT= 0 FV= 1025875.398 P/Y= 1 C/Y= 1 PMT: END BEGIN N= 20 I%= 8 PV= 0 PMT= -4000 FV= 183047.8572 P/Y= 1 C/Y= 1 PMT: END BEGIN
  • 28.
    • Problem 8f
    • Suppose Bob and Barb bought their home 10 years ago and made monthly payments as scheduled. They plan to move in two years. They could refinance for 7.25% right now on a new 20-year mortgage, but closing costs would be $1800. Should they refinance? Assume that they will roll over the closing costs into the new mortgage.
  • 29. N= 240 I%= 7.25 PV= 163322.53 PMT= -1290.86 FV= 0 P/Y= 12 C/Y= 12 PMT: END BEGIN N= 240 I%= 8.5 PV= 161522.5251 PMT= -1401.73 FV= 0 P/Y= 12 C/Y= 12 PMT: END BEGIN N= 360 I%= 8.5 PV= 182300 PMT= -1401.7292 FV= 0 P/Y= 12 C/Y= 12 PMT: END BEGIN Calculate the New Monthly Payment Calculate the Present Value Calculate Original Monthly Payment
  • 30. Yes, they should refinance. They will save $110.87 per month for about 7.8 months before they move. 16.235 months Number of months to recoup the closing costs? $110.87 Savings per month? $1,290.86 $1401.73 Monthly Payment? $163,322.53 $161,522.53 Present Value New Mortgage (7.25%) Current Mortgage (8.5%)
  • 31.
    • Problem 8h
    • Bob and Barb Noxious took out an $182,300 loan at 8.5% interest for 30 years for the purchase of a new house. The loan requires monthly mortgage payments. If, on the original loan, they paid an additional $100 per month, how long would it take to pay off the loan?
  • 32. Problem 8h: Additional $100: t = 278.4190833 months t = 23.2 years Years reduced = 6.8 N= 278.4190833 I%= 8.5 PV= 182300 PMT= -1501.73 FV= 0 P/Y= 12 C/Y= 12 PMT: END BEGIN
  • 33.
    • Problem 10a
    • Paige is offered two options when purchasing a new $17,000 car. Option 1 offers 6.75% financing for 4 years and $2500 “cash back.” Option 2 offers 4.75% financing for 5 years with no cash back. The financing requires monthly payments. Find the monthly payment for each financing option. Assume that the cash back in Option 1 will be used to reduce the amount of the original loan. If Paige’s goal is to pay the minimum amount for financing over the life of the loan, which option should she choose? Explain why using specific numbers
  • 34. Option 1: Interest = 48($345.54) – $14,500 = $2,085.92 Option 2: Interest = 60($318.87) – $17,000 = $2,132.20 Option 1 (the cash back option) is best since less interest is paid and the loan is paid off sooner. N= 60 I%= 4.75 PV= 17000 PMT= -318.87 FV= 0 P/Y= 12 C/Y= 12 PMT: END BEGIN N= 48 I%= 6.75 PV= 14500 PMT= -345.54 FV= 0 P/Y= 12 C/Y= 12 PMT: END BEGIN Option 2 Option 1
  • 35.
    • Problem 11b
    • Repeat the calculations of 11a to determine which car has the lowest cost to own, A Chevy Cavalier or a Toyota Camry. The Chevy Cavalier costs $21011 and has a residual of 26.3% after 3 years, and a Toyota Camry costs $29650 and has a residual of 63% after 3 years? Assume an annual interest rate of 8%, and that you will sell the vehicle at its residual value after three years
  • 36. $410.25 $420.78 Cost per Month $14,768.94 $15,148.06 Total Cost $18,679.50 $4,605.13 Residual Value 63% 26.3% Residual $33,448.44 $19,753.19 Total Payments $929.12 $548.70 8% 3-year loan pymt $29,650 $17,510 List Price Toyota Camry Chevy Cavalier
  • 37.
    • Problem 12a:
    • Dell has advertised a Dimension E521 computer for $1149 ($1218 after tax) or $35 per month. You are in need of a new computer and this model seems to satisfy all of your needs. Suppose that you pay only the minimum due of $35 (at 19.99% APR) each month on your new computer.
    • How long will it take you to pay off the computer? How much will you have paid on the $1218 balance when the computer is finally paid off?
  • 38. About 52.5 months or 4 years, 4.5 months; $1,837.50 N= 52.46684889 I%= 19.99 PV= 1218 PMT= -35 FV= 0 P/Y= 12 C/Y= 12 PMT: END BEGIN
  • 39.
    • Problem 13a:
    • In a $131,250 subprime loan with a 3/27 ARM, the initial interest rate is 8% and it will remain 8% for three years; at the end of the first three years it will increase to 12%. Complete the table below. For both a regular and interest-only loan, by how much will the monthly payment increase after the third year when the rate increases?
  • 40. $403.83 $366.65 Increase in payment $1,366.90 $1,329.72 Monthly Payment after 3 rd year $131,250.00 $127,680.20 Present Value of Loan after 3 years $0 $3,569.80 Principal Paid over 1 st 3 years $31,100.72 $31,100.72 Interest Paid over 1 st 3 years Varies: $875.00 down to $851.94 $963.07 Monthly Payments (first 3 years) Interest-only 3/27 ARM Regular 3/27 ARM
  • 41. Problem 5: Earn 32% Rate of Return the Easy Way. Many employers offer a 401K or 403B plan (tax sheltered annuity or TSA) that allows employees to invest for retirement. The beauty of the plan is that employees who invest $15,000 in a year, will pay federal taxes on $15,000 less in income – a tremendous tax savings. If we assume that the tax saved equals the rate of return on an investment, calculate the return on investment for the two employees below .
  • 42. 32% Rate of return: $4,800 Tax Savings: $3,200 $2,600 State Tax Paid (4%) $17,102 $12,902 Fed Tax Paid $80,000 $65,000 Taxable Income $0 $15,000 Investment in TSA $80,000 $80,000 Salary
  • 43.
    • Problem 9
    • Suppose that you are going to finance the purchase of a new $21,000 car. There are three financing options available to you: 1.9% financing for 3 years, 3.9% financing for 4 years, or 5.9% financing for 5 years. Compare the financing costs for each of the three loans. Which would be best for you and why?
  • 44. $3,300.78 $1,714.61 $620.80 Cost to Finance - Interest $24,300.78 $22,714.61 $21,620.80 Total payout during the term 60 48 36 Total Number of Payments $405.01 $473.22 $600.58 Monthly Payments 5 Years (5.9%) 4 Years (3.9%) 3 Years (1.9%) Loan Term $21,000 Car Loan
  • 45. Toward Quantitative Literacy: Interesting Problems in Finance Jim Ham http:// www.delta.edu/jaham 2008 AMATYC Conference Washington, D.C. Saturday, November 22, 2008 Thank You!