This is the story about 10 students (the STAT PACK) who areworking their way through lessons in money mathematics. They are serious students who progress to the point where they can, among many other things, calculate mortgage payments, understand the dangers of making minimum paymentson credit card bills, explain a financial retirement savings program, demonstrate how a Ponzi scheme works, and provide illustrations showing the advantages of starting to save early. Their leader in this educational adventureis Herkimer, a cartoon character who provides stimulating questions and activities to enhance the learning process. Her kimer is not the teacher, but he is always present when Pack members have discussions relating to money topics they are studying. He is a Hobbs-like character (for thosefamiliar with the Calvin and Hobbscomic strip) who is visible only to the Pack. Herkimer is not unfamiliar to the students since they had worked with him while learning basic statistics in a previous book titled THE STATISTICAL ODYSSEY OF HERKIMER AND THE STATPACK. A major reason for the financial crisis that began in 2008 was a lack of financial literacy in citizens of all ages. Author Sanderson M. Smith is a multiple award-winning mathematics teacher (including the California Presidential Award for Excellence in the Teaching of Mathematics and a California National Educator Award) who developed a FINANCIAL MATHEMATICS course at Cate School (Carpinteria, CA) many years ago. This entertaining and e
HERKIMER AND THE STAT PACK VENTURE INTO MONEY MATHEMATICS
By Sanderson M. SmithAuthorHouse
Copyright © 2009 Sanderson M. Smith
All right reserved.ISBN: 978-1-4490-1906-8Contents
INTRODUCTION......................................................................................................8Session #1: HERKIMER AND THE STAT PACK GET BACK TOGETHER..........................................................15Session #2: INTRODUCTORY DISCUSSIONS ABOUT FINANCE................................................................19Session #3: SINGLE DEPOSIT ACCUMULATION...........................................................................22Session #4: SINGLE PAYMENT DISCOUNTING............................................................................28Session #5: TRAPPING A FINANCIAL SOLUTION.........................................................................34HERKIMER'S QUICK QUIZ (Sessions 1 - 5)............................................................................39Session #6: PACK MEMBERS CREATE USEFUL FINANCIAL TABLES...........................................................40Session #7: THE CONCEPT OF FINANCIAL INFLATION....................................................................45Session #8: MULTIPLE DEPOSIT ACCUMULATION.........................................................................49Session #9: FINANCIAL SITUATIONS INVOLVING PAYMENT ACCUMULATIONS..................................................55Session #10: OTHER MULTIPLE DEPOSIT ACCUMULATION MODELS...........................................................59HERKIMER'S QUICK QUIZ (Sessions 6 - 10)...........................................................................63Session #11: SOME DEPOSITS DON'T FIT A NICE ACCUMULATION MODEL....................................................64Session #12: PRESENT VALUE OF FUTURE PAYMENTS.....................................................................68Session #13: MORE ON CALCULATING INVESTMENT YIELDS................................................................72Session #14: THE PACK PRODUCES MORE USEFUL FINANCIAL TABLES.......................................................76Session #15: OH! THAT EVER-USEFUL ALGEBRA.........................................................................81HERKIMER'S QUICK QUIZ (Sessions 11 - 15)..........................................................................85Session #16: THE ANATOMY OF A LOAN................................................................................86Session #17: INSTALLMENT PAYMENT FORMULAS ARE SOMETIMES USEFUL....................................................92Session #18: DON'T CONFUSE NOMINAL RATES AND TRUE RATES...........................................................97Session #19: MORE ON NOMINAL RATES................................................................................102Session #20: PAYMENTS AND INTEREST PERIODS MUST JIVE..............................................................107HERKIMER'S QUICK QUIZ (Sessions 16 - 20)..........................................................................112Session #21: LOANS WITH MONTHLY PAYMENTS..........................................................................113Session #22: MORTGAGES - THE BIG LOANS............................................................................121Session #23: MORTGAGES - COMPLETE PAYMENT SCHEDULES...............................................................127Session #24: THE CREDIT CARD TRAP.................................................................................133Session #25: CREDIT - A DANGEROUS WAY TO LIVE BEYOND YOUR MEANS...................................................140HERKIMER'S QUICK QUIZ (Sessions 21 - 25)..........................................................................145Session #26: BASIC CONCEPT BEHIND RETIREMENT PLANS................................................................146Session #27: A BIT MORE ON RETIREMENT PLANS.......................................................................152Session #28: SOME INSIGHT INTO BONDS..............................................................................157Session #29: YIELDS ON U.S. SAVINGS BONDS.........................................................................161Session #30: YIELDS ON COUPON BONDS...............................................................................167HERKIMER'S QUICK QUIZ (Sessions 26 - 30)..........................................................................171Session #31: AVOID PONZI SCHEMES..................................................................................172Session #32: PACK MEMBERS DO INDIVIDUAL PROJECTS..................................................................177Session #33: BRENDA'S PROJECT: THE RULE OF 72.....................................................................180Session #34: VALARIE'S PROJECT: PAYDAY LOANS......................................................................185Session #35: WAYNE'S PROJECT: START TO SAVE EARLY.................................................................189Session #36: DARRIN'S PROJECT: CONTINUOUS INTEREST................................................................194Session #37: FRANCES' PROJECT: ADVANTAGE OF EXTRA MORTGAGE PAYMENTS...............................................199Session #38: CAROLYN'S PROJECT: REFINANCING.......................................................................205Session #39: ROGER'S PROJECT: BOND AMORTIZATION SCHEDULES.........................................................210Session #40: STEPHEN'S PROJECT: INFLATION CONCERNS IN RETIREMENT..................................................216Session #41: GLEN'S PROJECT: TEASER RATES.........................................................................222Session #42: JANICE'S PROJECT; ADJUSTABLE RATE MORTGAGES (ARMs)...................................................227Session #43: THE PACK MAKES A LIST OF USEFUL FINANCIAL TABLES.....................................................233Session #44: HERKIMER AND THE STAT PACK: THE FINAL SESSION........................................................241HERKIMER'S FINAL FINANCIAL TEST...................................................................................246APPENDIXES........................................................................................................256APPENDIX A (Algebraic Derivation of Formulas).....................................................................257APPENDIX B (A complete 30-year mortgage schedule and a complete credit card payment schedule).....................260APPENDIX C (Solutions and comments for selected activities).......................................................271INDEX OF TERMS (By session number)................................................................................294
Chapter One
Session #1 HERKIMER AND THE STAT PACK GET BACK TOGETHER I must say I hate money, but it's the lack of it I hate most. -Katherine Mansfield
It was a joyous reunion when Herkimer made his appearance before the Stat Pack. For those not familiar with the former association linking him to this group of young people, Herkimer had previous mathematical encounters with the ten students who were introduced in the book:
THE STATISTICAL ODYSSEY OF HERKIMER AND THE STAT PACK
Herkimer had provided guidance, advice, and educational activities as the students worked their way through an introductory statistics course. He loved the fact that the students had created a group name, the Stat Pack. When the Pack completed the statistics course they knew that Herkimer would disappear from their lives and that he would attempt to find and help another group of dedicated students who were about to undertake a study of basic statistics. Herkimer did not anticipate ever seeing the Pack again.
It was through association with Herkimer that the Pack came to realize that understanding the language of statistics was the real key to success in the subject. Herkimer often stressed the theme that mathematics is a language. He believed that far too many students fail to realize this simple fact and do nothing more than attempt to memorize procedures and formulas. Some Pack members reflected on previous math courses they had taken and realized that this is exactly what they had done. Herkimer had "opened their eyes" to the realization that learning mathematics involved much more than rote memorization. They came to appreciate that mathematics was indeed a language that had been developed over a period of 2000 years as humans struggled to understand and comprehend the universe in which they existed.
As they began thinking and talking about moving on to college and post-teen years, Pack discussions began to center around financial concerns. They realized that they would have to assume more responsibility for handling money and related items like credit cards. Always alert to current events, they were quite aware of the financial woes encountered by many adults. The time was early in the 21st century and Pack members, even at their young age, were aware that the United States was in the midst of a financial crisis. In fact, they knew the crisis was global. Terms such as bankruptcy, meltdown, foreclosure, bailout, and bear market dominated the news. And, they came to realize that they knew very little about how money works in a capitalistic society. While they all had studied statistics and some had taken a calculus course, they were provided no opportunities to take courses in financial mathematics and money management.
Will Rogers once said, "We are all ignorant, only in different subjects." As they were once ignorant about statistics, Pack members acknowledged that they were presently ignorant about finance. Some of them had listened to their parents moan over the fact that their mortgage payments had recently increased. Some knew people who were coming to grasp the reality of the fact that they were over their heads in credit card debt. The Pack knew that it was possible to buy items without paying cash and that it would be very easy to overestimate an ability to pay for these things when it came time to "pay up." But this group of youngsters realized that other than infrequent advice offered by parents they had no real experience with money management.
One of the group mentioned Herkimer and the statistics education they had received from him. Another wished aloud that Herkimer could somehow return to help them in developing an understanding of financial mathematics. This feeling was unanimous. The Pack had a genuine desire to gain knowledge and insight into how money works in a capitalistic society, but they were certain that they had seen the last of Herkimer.
They sat in silence for a brief period of time. Suddenly an eerie sense of restlessness gripped the group. For a brief moment they all knew something was about to happen.
At that moment, Herkimer reappeared.
When the student is ready, the teacher shall appear. (Chinese proverb)
ACTIVITY SET FOR SESSION #1
1. ALCAL activity: The primary purpose in this activity is to emphasize an understanding of the order of operations as referenced in the INTRODUCTION. In each situation, evaluate the given numerical expression without any calculator use. Then use the calculator representation to check your responses:
2. REFLECTION & COMMENT activity:
It is important for you to know where you are and where you want to go.
(Common financial proverb)
3. Research the Internet for information relating to financial education. Using a search engine and typing in phrases such as lack of financial education will produce some interesting and eye-opening results.
4. There are numerous categories of financial education that are important to American citizens. Four of these are (a) basic savings; (b) credit management; (c) home ownership; (d) retirement planning. Does your local school system provide education in these and other areas of finance?
5. Keeping in mind that some adults lack money management skills, what role should parents play in developing financial literacy for their children? $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
Chapter Two
Session #2 INTRODUCTORY DISCUSSION ABOUT FINANCE When a fellow says it hain't the money but the principle o' the thing, it's th' money. -Frank McKinney Hubbard
The Pack members were intelligent and curious students. They took time each day to keep up on current events. They were aware that a mortgage crisis was a major concern for the United States in the early years of the 21st Century. Always the optimist, Herkimer started out by saying that this crisis may well create momentum for improving financial literacy in the U.S. educational system. "Hey, it's about time," he said. "Too many people of all ages simply do not know how to manage money."
Herkimer went on to explain to the Pack that the need for financial knowledge has increased drastically in recent years. If one looks back 30 or 40 years, one finds people who shopped primarily with cash, had fixed-rate mortgages, and relied on company pensions for retirement. In modern times citizens of the United States have been introduced to a world of credit cards, adjustable rate mortgages, and a variety of pension problems along with uncertainty relating to the future of social security.
Herkimer also noted that some high schools offer courses that teach students how to balance a checkbook or follow the stock market, but only 18 states require some type of instruction in personal finance. Very few people know how an annuity works. And, it is also a fact that many highly educated people aren't financially literate and rely on so-called financial advisors for advice relating to investments and money matters.
"Financial literacy is a necessity in planning for retirement, for understanding how investment money grows, for managing debts, and for credit card management," said Herkimer as he began writing a question on the chalkboard. He mentioned a recent study indicating that only 18% of American adults questioned were able to produce a correct response to the question.
The challenge was before them. Pack members started punching numbers into their calculators. After about 30 seconds, Stephen asked, "I get $3,000, is that right?"
"No, responded a grinning Herkimer," but that is the amount given by 34% of the adults who responded to the question. A sad fact is that 82% of the adults answering the question either got that answer, got another wrong answer, or simply didn't respond."
"I got $3,000 too," volunteered Glen. "Let's get started on gaining financial literacy," he continued. "It seems like we really need it."
ACTIVITY SET FOR SESSION #2
1. ALCAL activity: In each situation, evaluate the given numerical expression without any calculator use. Then use the calculator representation to check your responses: To be evaluated Calculator entry Number represented
2. REFLECTION & COMMENT activity:
It's not the government's role to save someone who is in debt because they went to the mall and charged thousands on their credit card. When many people budget, they start by thinking how to reduce their lattes or cable TV service. What's more important is to focus on the big expenses you need to pay each month, with about 50% of your income going toward that. Another 30 percent should could towards "flexible" costs including eating out, clothing, vacations and hobbies. Save the remaining 20 percent. That means consider housing needs before wants.
(Elizabeth Warren, Harvard Law Professor, "champion for consumers")
3. Can you provide the correct answer to the question posed by Herkimer in this vignette? (Answer will be provided in Session #3.)
4. Far too many Americans don't seem to understand the simple concept of not spending more than they earn. One major reason for this is that people think of credit cards as assets. Research the recent explosion of credit card use in the United States. Are credit card companies to blame for the considerable credit card debt in this country? Or, should the blame for this problem be attributed to a lack of basic financial education? (Sessions in this book will provide details relating to credit card use.)
5. What does it mean to say that a major cause of the financial turmoil in the early 2000's resulted from mortgage loans that were made to shaky borrowers? (Sessions in this book will discuss mortgage loans.)
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Chapter Three
Session #3 SINGLE DEPOSIT ACCUMULATION The safest way to double your money is to fold it over once and put it in your pocket. -Frank McKinney Hubbard
It was a new day but Herkimer quickly returned to the perplexing problem of the previous session. He placed this transparency on the overhead.
If you have $2,000 in an investment earning 10% a year and simply let the money grow, how much would you have at the end of 5 years?
"OK," began Herkimer, "I bet those of you who came up with an answer of $3,000 probably calculated ($2,000)(0.10) = $200 interest per year and concluded that in 5 years the interest earned would be ($200)(5) = $1,000. Hence the value of their investment would be $2,000 + $1,000 = $3,000."
"Yup, that's what I did," responded Stephen.
"Me, too," chimed in Janice.
"Your responses are not without merit," said Herkimer. He explained that $3,000 would be a correct response if one is working with simple interest, where annual interest is calculated only on the initial investment. But Herkimer stressed that this is not the way money usually works in our capitalistic society. Simple interest does not take into account the power of compounding. Using compound interest, the $2,000 investment would accumulate to $2,000 + (0.10)($2,000) = $2,000(1 + 0.10) = $2,000(1.10) = $2,200 at the end of 1 year.
Always ready to emphasize the importance of basic algebra concepts, Herkimer placed this transparency on the overhead.
BASIC ALGEBRA: a + ab = a(1+b). In general, ca + cb = c(a+b).
He went on to explain that one now starts the second year with $2,200. This new amount earns 10% annual interest. So, your investment value at the end of the second year is valued at $2,200 + (0.10)($2,200) = $2,200(1.10) = $2,240.
Herkimer wanted to emphasize the algebra involved and leading up to an important general formula so he slipped this transparency on the overhead below the one already there.
The total interest earned at the end of the second year is $2,240 - $2,000 = $240.
"Oh, I get it," bellowed Glen. The Pack watched as Glen took his calculator to the chalkboard and wrote the following:
YR ACCUM
0 $2000 1 $2000 (1.10) = $2200.00 2 $2000 [(1.10).sup.2] = $2420.00 3 $2000 [(1.10).sup.3] = $2662.00 4 $2000 [(1.10).sup.4] = $2928.20 5 $2000 [(1.10).sup.5] = $3221.00
"You got it," replied Herkimer. "OK, now you guys learned how to use spreadsheets when we were studying statistics. Split up in pairs and see which team will be the first duo to produce a spreadsheet that will display the growth of single deposit of $2,000 for 10 years at both simple and compound annual rates of 10%." While column headings (A, B, C, ...) and row headings (1, 2, 3, ...) are often omitted when spreadsheets are printed out, Herkimer asked the Pack to include these on their displays. "After a few sessions we will not print out these headings," he continued, "but we will do so initially since they might be useful to a teacher who might want to use them to illustrate spreadsheet commands to students."
From their statistics experience the Pack knew how to determine five teams of two students through a random process. Once this was done, the teams moved to the available computers and started working on the project. After about 10 minutes the team of Carolyn and Wayne produced this display.
Herkimer asked the Pack to use their calculators to check the computation displayed on the spreadsheet. It was agreed that at the end of the 10th year with compound interest, the accumulation would be $2000[(1.10).sup.10] = $5187.48. The interest earned would be $5187.48 - $2000 = $3187.48.
"OK," said Herkimer. "As we move on, we are going to assume that we are working only with compound interest rate. This will be the first and last activity set to address the concept of simple interest. For now let's have all of you work up a spreadsheet relating to the accumulation of a single deposit.
Brenda came up with this spreadsheet display.
"That is a fabulous display," said Herkimer. "It clearly illustrates the power of compounding. Brenda's spreadsheet shows that at 7% money will double in 11 years, triple in 17 years, quadruple in 21 years, and increase 5-fold in 24 years. This should serve to illustrate that if you are young and are thinking about saving for retirement, the sooner you get started, the better."
ACTIVITY SET FOR SESSION #3
1. ALCAL activity: Use your calculator to check the interest earned total on Brenda's spreadsheet:
2. REFLECTION & COMMENT activity:
Unfortunately, we have found that the vast majority of people we deal with are more concerned with making money than with understanding how to make more efficient use of the money they already have. (Money Mastery, by Williams, Jeppson, and Botkin)
3. Assume someone unfamiliar with financial matters asks you to distinguish between simple interest and compound interest. How would you respond?
4. Consider a single deposit of $1,000. What would this investment be worth at the end of 20 years (a) at a simple interest rate of 5% a year? (b) at a simple interest rate of 10 % a year?
5. Consider a single deposit of $1,000. What would this investment be worth at the end of 20 years (a) at a compound interest rate of 5% a year? (b) at a compound interest rate of 10% a year?
6. Respond TRUE or FALSE.
(a) At a simple interest rate, a single deposit earning an annual rate of 10% will earn exactly twice as much interest as the same deposit earning an annual rate of 5% over a period of two or more years.
(b) At a compound interest rate, a single deposit earning an annual rate of 10% will earn exactly twice the interest as the same deposit earning an annual rate of 5% over a period of two or more years.
7. Since $1[(1.05).sup.14] = $1.98 and $1[(1.05).sup.15] = $2.07, money will double ($1 will grow to $2) in 15 years at annual compound interest rate of 5%. Complete the doubling-time table for the indicated annual compounded interest rates.
(Continues...)
Excerpted from HERKIMER AND THE STAT PACK VENTURE INTO MONEY MATHEMATICSby Sanderson M. Smith Copyright © 2009 by Sanderson M. Smith. Excerpted by permission.
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