Math Matters: Why Do I Need To Know This?


 Bathsheba Shelton
 3 years ago
 Views:
Transcription
1 Math Matters: Why Do I Need To Know This? Bruce Kessler, Department of Mathematics Western Kentucky University Episode Fourteen 1 Annuities Investment strategies Objective: To illustrate how knowing the mathematics behind annuities can help us to understand and calculate the future value of investments. We also illustrate how small changes in our contributions now can cause a large difference in the future value of our investments. We develop the formula for the sum of a geometric series, and the formula for the future value of an annuity. Hello, and welcome to Math Matters: Why Do I Need To Know This? This is our last episode of Math Matters, and we, we... it s been a lot of fun. I enjoy getting the opportunity to talk about the applications of mathematics, and hopefully it s been an educational process for all of us. I want to finish today with just a couple ideas from consumer mathematics, things that don t require heavy duty mathematics in order to understand, but it s good for you to know, so that you can kind of plot your course through life, planning your money and so forth. And then I ll kind of wrap up at the end. So let s get going. I d like to talk to you about annuities, and first I should probably start and tell you what an annuity is. An annuity is any type of account, a savings account kind of thing, where you make a regular payment into the account, and then you get interest on the... not just the, you re doing more than just getting money out of it, you re accruing compound interest on this money that you put into the account. Examples would be IRA s, individual retirement accounts, or other types of retirement plans, where you re making a regular contribution. Things like wholelife insurance policies, not term, but wholelife, where you pay on this, and then it has some value when you re done paying on it. And even little things, like Christmas Club accounts where you, you put money in monthly and then in December you get the money out and you take that and you go shopping with it, or something like that. Lets take a look at the timeline of how things work, I want to describe to you how to calculate the value of these things, and to do that, lets talk about how these things would work. You would typically think about in the timeline, and these are the are months, this is segmented in months, so somewhere here you set this thing up, and then at the end of the month, typically out of your paycheck, you ll make a contribution. So let s assume we re making a hundred dollar regular payment into the annuity, which would be made at the end of the month, okay? Now, how much is that going to be worth when we re done? Makes sense it would be about $400, right? I m making four $100 payments, so my answer should be somewhere close to or slightly above $400. The way to kind of get to the future value of this after a period of time is to take that monthly rate, we ve done this before, this is the compound interest formula, it s 100% of what you have, plus the monthly rate, and you re going to compound that interest, but, in this first month, you only draw one, two, three months of interest on it, so thats raised to the third power. The second payment only receives two months of interest. So thats a two right there, the third payment only receives one month of 1
2 interest, and the fourth receives no interest at all, it s just the one hundred dollars that you started with, and I went ahead and put the zero there, to kind of illustrate what s happening. To get to the future value of this we have to add these amounts up. (Figure 1) Figure 1, Segment 1 So you re adding up things raised to powers. Now, that can, you can do that the hard way, I mean you get your calculator out, and just sit there and huntandpeck all the time, but I d like to look at things that happen over a long period of time, so i need a formula, I need a short cut to the answer. So what I m going to do is, I m going to show you a little trick, this is a cool little trick, where we add up things. What we re talking about, when we add up things raised to an increasing power it, we call that a geometric series. And we have a nice way of generating the value of a geometric series. I m going to show you the trick. This is really slick. Let s say I want to determine what this would add up to, you know, r is some number, and I m raising to the zero power, and the first power, you know, adding it up, and adding it up, and take this to the nth power. I add all these things up. Well let me call this S, okay? I don t know what S is, thats what I want to find out, and I m going to pull a little stunt here, I m going to multiply S by r. Now what that does, is it raises the power by one. So I m lining things up here in powers of r. And then I will subtract this, from that. So subtract, subtract, I ll even put the little bar there. When I subtract these things, I get S rs, and I can factor out that S. Over here the r 1, the r 2, the r to the whatever, even the r n cancel each other out. So, I m just left with r 0, which is 1, minus r n+1. And so to solve for S, I just divide through by the junk, standard little trick. It actually, the way I set it up, it ends up being one minus this, and one minus that, but if you multiply by 1 in the top and the 2
3 bottom, it would look like this, where you subtract the one in each case. And that looks a little neater in the formula I m getting ready to develop. (Figure 2) Figure 2, Segment 1 I m going to use this idea now to calculate the future value of that account. So we go back to this, where I ve got all the different accounts, all the different payments put in, and the compound interest that they, that they draw, I m going to add those things up. So each one of those has a one hundred there that I can factor out, k, and then here is my geometric series. And if you ll notice, that power of r is always one more than the highest power in the series. So this would be a four, which is actually equal to the number of payments I made, okay, and then it s just a matter of deciding what the monthly rate is. I do this with, uh, oh, there is a little simplification, one plus M minus one is just M. If I assume a 6% interest rate, that s 6% annual, divide that by twelve, then thats 1 % per month. So my monthly interest 2 rate would be And then, when I do the little calculation, it works out to be $ So that means I gained $3.01 from this process, other than just what I paid in. Not a big wad of money, I know. (Figure 3) But now lets think about, I d like to think about what happens if I try to do this over a long period of time. So, first let me say that the general formula, let me just go back, and I ll take the onehundred, make that a P, n is the number of payments, okay? So here s the formula that I would use to calculate the value of the annuity after so many payments. Let s say for example that I pay a hundred dollars from each paycheck for thirty years. And I ll say still I m getting 6%, okay? So, taking those amounts, here s the 100, there s the 1% 2 interest, there s the 1 % interest. When I do that calculation, I end up with over $100, Now, when you think about how much I paid in, I paid in $100, 360 times. So thats $36,000 3
4 Figure 3, Segment 1 that I paid in. I ve almost tripled my money by doing that over a long period of time, okay? You know, I m trying to show you the value of this kind of account. (Figure 4) The additional thing to kind of point out about this, is how it reacts to small changes. Now, lets say instead of $100, I put in $101. That means I m going to contribute an additional $360, okay? So, how does that affect the calculation? Well, it raises it by a little over $1,000, so again, I put in an extra $360, I get out an additional $1,000. I could also look at changes to the percentage rate. One percent of $36,000 is $360. However, compound interest works so that I draw interest on my interest, and that snowball effect, if I raise this up to 7%, as opposed to 6%, the end value, the future value of this account, is $142,330, basically, thats a 41, or $42,000 increase. That that s dramatic, okay? So it shows how affected that is by the interest rate. (Figure 5) I ve actually got a couple of summary pages that have those formulas on them, that will kind of summarize what we just talked about, and I ll get us setup for the next segment. 4
5 Figure 4, Segment 1 Figure 5, Segment 1 5
6 Summary page 1, Segment 1 Summary page 2, Segment 1 6
7 2 Fair division Estate settlement Objective: To illustrate how some very simple arithmetic can be used to divide an estate with several nondividable objects in a fair manner among several heirs. The idea I d like to talk to you about today involves the fair division of estates. Perhaps you ve inherited some money, or you ve inherited a house, or a boat, or things like this, and you have siblings, so you have to share it. Well, some things share very well. Money, you can take a wad of money, if there s three of us, we divide by three, we each take that amount of the money, and we go with it. It s not so easy when I talk about things like houses, and boats, and so forth. You can cut them into thirds, but then you ve destroyed the value of them. You can sell things, but, thats not always a good option either. If it s the old family home, you don t want to sell the old family home, you know, you want to, someone needs to hold on to the possession of that in the family. And so the question becomes how do you divide things up so that everyone feels like they are getting their fair share of the estate. And it turns out there s a nice little mathematical algorithm for doing this that I m going to, I m going to take you through. It s very simple; it really just involves addition and subtraction, and division and so forth, but it s pretty slick. Let me run this situation by you, lets say there are three heirs to an estate, that includes a house, a boat, a car, and then there s $75,000 in cash. Okay, now the cash division is easy, they ll each, you know we can say you ll each get twentyfive thousand of that. But let me hold on to that cash for just a moment, and let s talk about how we can divide the estate up fairly, okay? The first thing I would do if I m trying to work this problem is I would say, okay, I would like each of the heirs to bid on the items. And this will take place in complete secrecy, and I ll show you later, that it actually works to their advantage to bid on it s value to them, not some kind of inflated value. So, we go through, and all the heirs bid on the items, and I m showing you some examples of what those bids could be. (Figure 1) Then what we need to do is go through, and, based on these bids, determine what they would consider to be a fair share of the estate. And the way we do that is we add up the value of everything according to what they called the value. So for Heir 1, we take the values that they gave here, add those up, and then the $75,000 is worth $75,000 to everybody, so we add that up, and that makes the estate worth $168,000 to this heir. We re going to share it equally, so we divide by three, and that gives us what we call their fair share, according to them. We do this to each of the three heirs, so we do this across, we add everything up, divide it by 3, add everything up, divide by three, so they re being fairly consistent here, but they re not identical, and that s kind of important. But this is what every one of them should consider a fair share of the estate, okay? (Figure 2) Then, we go in and we say, okay, you bid the highest for this item, you consider it to be the most valuable item of the three of you, so you get that item. Now in our case here, that would mean that Heir 1 gets the house, Heir 2 bid the highest with $7,000 for the boat, and Heir 3 bid highest on the car, so they get the car, okay? You get those items. Now here s the problem: this house is valued at, actually by all of them, at much more than their fair shares. These are valued much less than their fair shares. (Figure 3) So what we do is we then use the cash, that s in the account, to kind of adjust everybody down to the fair share, okay? So the first person, the house is worth more than their fair 7
8 Figure 1, Segment 2 Figure 2, Segment 2 8
9 Figure 3, Segment 2 share, that means they need to pay some back, and they end up paying the difference, which is $29,000. That s paid into the estate, okay? Now the folks paid, they received less than their fair share, so we re going to make up that difference in cash, okay? So, Heir 2, when we subtract, they would receive $48,000, paid from the estate. That s removed from the amount of cash we have on hand. And Heir 3 received the car I think. That difference in their fair share, what they consider their fair share, and the cars value, what they consider the cars value, is $47,000, so we take that out of the estate, pay that to them. And when we re all done with this, we still have a little bit of money left over. There s nine thousand dollars left out of the cash. (Figure 4) And so the next step is easy. Divide 9,000 by three, give each of the people left, give each of them what s left, $3,000 to each of the heirs. So what does that really give, what do they end up with, that s kind of the point of this. The first heir gets the house, which they value at $85,000. They had to pay some cash, but they get $3,000 of it back, for a grand total of, in their mind, $59,000. Okay, now that s $3,000 more than what they considered to be their fair share. The second heir got the, I think it was the boat, received some cash, and received the additional cash. That additional cash is over and above what they considered to be their fair share. And then the third heir, the same thing happens. This is the system, because everybody ended up getting more than what they considered to be fair. Everyone should be happy with this arrangement. Which is nice, that s a good system, that s a good way to kind of handle things. (Figure 5) Even beyond that, it s a good system in that it discourages folks from bidding artificially, you know, to make sure they get it. Everyone has to play honest, or they re going to get 9
10 Figure 4, Segment 2 Figure 5, Segment 2 10
11 caught, and I ll show you how that works. Let s say that the first heir really, really, really wanted the house. So they gave this exorbitant price, this exorbitant bid on the house. Even though they really thought it was valued at $85,000, they bid $200,000 on it, okay? Now watch how this effects their totals. Their fair share now is going to go up, right when I change this to $200,000, the value goes up here, and then when you divide by three, it goes up. So, their fair share is inflated as well, okay, the rest of them stay the same. (Figure 6) Figure 6, Segment 2 They were going to get the house anyway, and so they still get the house. What changes now though, is how much is paid to the estate. If this is twohundred thousand, this is now a pretty big sum, right? This is way over and above what they considered their fair share. So they have to pay quite a bit back to the estate, and what that does is that puts a lot more cash on hand for the estate, okay? (Figure 7 and 8) Everything else is as it was, but what changes is, instead of taking the amount $9,000, dividing by three, and getting $3,000, now when you divide by three you get $28,556. (Figure 9) So that s paid out, and watch what happens to the value here with each of the heirs, okay? And what I ve done is, instead of the $200,000, I used the actual value, what they thought it was actually valued at. They end up with a lot less than the others. And what they ve done is they cheated themselves out of, they did get the item they wanted, but they cheated themselves out of actual value of the estate. (Figure 10) This is a remarkable little system for doing this. Chances are at some point in your life, you might encounter a situation like this. Now you kind of have an idea how to handle the mathmatics of it. I ve summarized the algorithm for this in a couple of summary pages, and I ll get set up for the last little segment. (Figure 10) 11
12 Figure 7, Segment 2 Figure 8, Segment 2 12
13 Figure 9, Segment 2 Figure 10, Segment 2 13
14 Summary page 1, Segment 2 Summary page 2, Segment 2 14
15 3 Wrapup The last thing I d like to do with you today, since it s our last episode, is I would like to kind of wrap things up, and end with some encouraging words. Now I realize, at this stage of the game, you re probably getting ready for finals, you may be getting ready for finals, and you may even be a little sick of mathmatics at this point if you re finishing up the semester. But I would like to encourage you to follow up, and take some more mathmatics. And I have a couple of reasons for telling you this. We ve already demonstrated that we could handle some very tough situations with the mathmatics that we find in the general math courses. We ve looked, we spent a semester looking at things like that. It s also true though, that you can get into some fairly routine situations that have tough mathmatical answers, and that s the kind of thing that we handle in the upper level courses. For example, here s a very easy problem. If I say okay, what are all the solutions to this equation, well, you ve probably realized by now that that s a line. It s a linear equation, so the graph of that is a line, and the solutions are all the points on that line. That s pretty easy, a graphing calculator can do that for us. (Figure 1) However, if I ask the question this way, I say, what are the integer solutions to that equation? That is a lot less exacting. And, a lot of the solutions here will not work. They have to fall along an integer lattice here, like these points do. This one actually occurs at (1, 1), this one occurs at ( 2, 3). Those are integer solutions, they re not always, not everything on the line though will work for this answer. And so we re getting into a field of mathematics called discrete mathematics, and that requires some further study, although that s a very, that s a very simple kind of question. (Figure 2) Figure 1, Segment 3 15
16 Figure 2, Segment 3 Here s another one. Let s say I want exact solutions to this quadratic equation. Now you folks have probably had, know the quadratic formula, some of you even, I had some kids yesterday singing me, singing me the quadratic formula, which I thought was pretty cool. We have a way to do that, and I ll show you the graph. We use quadratic formula, we can even factor this one if we need to to solve it exactly. (Figure 3) However, if I take anyone of those powers up above 2, if I make that 2 a 3, that becomes a very difficult thing to solve symbolically. Even this one, which has nice answers, it has nice integer answers 2 and 1. If you ask me to do that symbolically, that all of a sudden becomes a pretty difficult problem, because I don t have a cubic formula. I have a quadratic formula. I know how to solve linear things, but something like that is actually kind of tough. We can talk about numerical solutions, we can talk about some different ways of trying to factor that, but as a rule, multiplying is much easier than factoring. And that s fairly difficult to factor. (Figure 4) That, by the way, is the idea behind public key encryption that you have this big long number that is the product of two primes. It s easy to multiply the primes together. It s very difficult to divide that composite number into the two primes, and that s, a lot of our national security is based on that very idea right there. Here s something else, if we look at two lines, a system of equations, linear equations, well, we ve talked about actually in this program ways of solving that exactly, you know, getting exact solutions to that. The solution will be this point where the two lines overlap. (Figure 5) However, if I jump above the power of one on any one of these things, like I make that x 3, make that y 4, all of the sudden, this has become an extremely difficult problem to solve exactly. And it really doesn t get much better as you go up the higher level mathmatics, this is just a hard problem, okay? Now, we can do it graphically. Obviously, I can graph 16
17 Figure 3, Segment 3 Figure 4, Segment 3 17
18 these things, and I can numerically isolate that point, and there are other techniques for doing that. But exact solutions are very difficult for nonlinear systems. So, these are the kind of things that can pop up, and, and in daytoday applications, I mean not everything is linear, thats just the sad fact of things. (Figure 6) Figure 5, Segment 3 Here s another example of a very tough problem. It sounds very simple. We have a bakery that makes five different types of fudge you know it sounds like something you would ask out of just being naive how many different ways can we fill a package with twelve pieces of fudge? I ve got five, I can make them all one type, I can make them all the other types, make half,.... I mean, you start thinking about all the ways to do this, and there are a lot of ways to do this. That is a very difficult question to answer. That s also something we d handle in the field of mathematics called discrete mathematics. We have counting techniques for doing things like that. But it s a little difficult. If I go back and say, well okay, let me put a restriction on that. Let s make sure we have one of each type in the package, then it gets just that much tougher to kind of figure out, okay, well, how many ways can you do this? You certainly don t want to try and list them all out by process of elimination, because the answer could be up in the thousands, tenthousands, whatever it is, okay? So this is some fairly difficult mathmatics to deal with, although it s very simply stated, okay? (Figure 7) The other kind of approach, the other kind of thing I would say as far as why I would encourage you to continue to study math is, you know, I think we jump the gun sometimes when we re studying, and we make this assumption that because we can t immediately find some applications for things, that it s not really very useful, okay? I couldn t disagree with that attitude more, okay? The problem sometimes is not in the mathematics, it s in our 18
19 Figure 6, Segment 3 Figure 7, Segment 3 19
20 understanding of other sciences, or other applications, the actual content where it could be applied, the area where it could be applied. You know, I always think back, a great analogy for this would be the space program, okay? The space program really kind of was driven initially by this fear of the Soviet Union dropping bombs on us from space and all this, but even after we had kind of won the cold war, we continued with our space program. People said now why would, why do we care about that now, you know, we won. But you have to look at the benefits that have come from that space program. Cell phones are a direct benefit, cell phones were actually developed through technology developed by NASA, in getting people to the moon and things like that. Velcro was designed after sticktights in nature. But where did they use that? Well, they use it in space capsules because you can t lay a pencil down in space, it floats off. So they needed a little piece of velcro, and a little piece of velcro, and they d stick it to stuff, okay? So, it really, it s not always the mathematicians fault, or the mathematics fault that we don t see the application. Sometimes we need to educate ourselves in other areas, okay? Terry Wilcutt I heard him say this one time Terry Wilcutt is an astronaut, who graduated from Western with a degree in mathematics, we re very proud of him he said Mathematics is the common language of the sciences. And that s true. If you re working in the science area, and you understand mathematics sometimes it would be very difficult for a biologist to talk to a geologist, for example, they may not have common things there but a mathematician, in some sense, in some way could probably talk to both of those people, as long as we re working on some kind of a problem together. I really would encourage you not to give up, even if you ve had a rough time this first time through. There s very cool stuff out there, and it just takes a little more education sometimes to find it. I ve summarized a few of those little comments that I talked about, and I ll flash those pages up, then we ll come back and wrap things up. Closing Well, I want to thank you for tuning in. I hope you ve checked out several of the episodes this semester. I hope they ve been helpful to you. I hope they ve been educational, and I hope they have served your purposes, helped you in class, and helped kind of expand your horizons as far as what math is good for. There s a lot of things out there. I still would like to hear your input on things, and would encourage you we have a webpage that we ll flash up in a few minutes use me as a resource if you wish to, to tackle things about applications, and you know I m always looking for new ideas around these lines. So, I want to to thank you for your time. I think I ve done all the damage that I can do, and I hope to see you again. 20
21 Summary page 1, Segment 3 Summary page 2, Segment 3 21
Math Matters: Why Do I Need To Know This? 1 Surface area Home improvement projects with paint
Math Matters: Why Do I Need To Know This? Bruce Kessler, Department of Mathematics Western Kentucky University Episode Six 1 Surface area Home improvement projects with paint Objective: To illustrate how
More informationMath Matters: Why Do I Need To Know This?
Math Matters: Why Do I Need To Know This? Bruce Kessler, Department of Mathematics Western Kentucky University Episode Nine 1 Normal distributions Statistical models Objective: To explain and illustrate
More informationMath Matters: Why Do I Need To Know This? 1 Probability and counting Lottery likelihoods
Math Matters: Why Do I Need To Know This? Bruce Kessler, Department of Mathematics Western Kentucky University Episode Four 1 Probability and counting Lottery likelihoods Objective: To demonstrate the
More informationMath Matters: Why Do I Need To Know This? 1 Amortized loans Monthly mortgage payments
Math Matters: Why Do I Need To Know This? Bruce Kessler, Department of Mathematics Western Kentucky University Episode Eleven 1 Amortized loans Monthly mortgage payments Objective: To illustrate the role
More information0:00:29 Kim: Thank you Todd, happy to be here, looking forward to talking about selfdirected
0:00:18 Todd: Hey everybody, welcome to another edition of The Prosperity Podcast, this is No BS Money Guy Todd Strobel. Once again, we have cohost and bestselling financial author Kim Butler in the house
More informationWholesaling Mark Ferguson
TRANSCRIPT OF EPISODE 14 OF THE INVEST FOUR MORE PODCAST Wholesaling Mark Ferguson Mark: Hi everyone. Mark Ferguson here with another episode of the Invest More Real Estate podcast. Today is just going
More informationMath Matters: Why Do I Need To Know This? 1 Logical fallacies Spotting bad arguments
Math Matters: Why Do I Need To Know This? Bruce Kessler, Department of Mathematics Western Kentucky University Episode Three 1 Logical fallacies Spotting bad arguments Objective: To illustrate the relevance
More informationWhole Life Insurance is not A Retirement Plan
Whole Life Insurance is not A Retirement Plan By Kyle J Christensen, CFP I decided to write this article because over the years I have had several clients forget how their whole life insurance fits in
More informationFinance 197. Simple Onetime Interest
Finance 197 Finance We have to work with money every day. While balancing your checkbook or calculating your monthly expenditures on espresso requires only arithmetic, when we start saving, planning for
More informationMath Matters: Why Do I Need To Know This? 1 Matrix Multiplication Complicated probabilities
Math Matters: Why Do I Need To Know This? Bruce Kessler, Department of Mathematics Western Kentucky University Episode Thirteen 1 Matrix Multiplication Complicated probabilities Objective: To illustrate
More informationClub Accounts. 2011 Question 6.
Club Accounts. 2011 Question 6. Anyone familiar with Farm Accounts or Service Firms (notes for both topics are back on the webpage you found this on), will have no trouble with Club Accounts. Essentially
More informationThe Reinvestment Assumption Dallas Brozik, Marshall University
The Reinvestment Assumption Dallas Brozik, Marshall University Every field of study has its little odd bits, and one of the odd bits in finance is the reinvestment assumption. It is an artifact of the
More informationGeometric Series and Annuities
Geometric Series and Annuities Our goal here is to calculate annuities. For example, how much money do you need to have saved for retirement so that you can withdraw a fixed amount of money each year for
More informationCOLLEGE ALGEBRA. Paul Dawkins
COLLEGE ALGEBRA Paul Dawkins Table of Contents Preface... iii Outline... iv Preliminaries... Introduction... Integer Exponents... Rational Exponents... 9 Real Exponents...5 Radicals...6 Polynomials...5
More informationAnytime Adviser New Car Buying Coach
Anytime Adviser New Car Buying Coach Welcome. This interactive guide offers you strategies for getting the best deal on a new car. Let's begin. Interested in a little guidance to negotiate your best deal
More informationScripts for Recruiters
Scripts for Recruiters Companion Script Guide for The New Recruiters Tool Kit www.greatrecruitertraining.com Copyright 2010 Scott Love 1 How to Use This Guide Use this companion script guide while watching
More informationDrunk Driving Vocabulary Lesson
Hello and welcome to the vocabulary lesson for the conversation Drunk Driving. In this conversation, Joe and I are just talking about different friends or different people that we ve known that have gotten
More informationLesson 4 Annuities: The Mathematics of Regular Payments
Lesson 4 Annuities: The Mathematics of Regular Payments Introduction An annuity is a sequence of equal, periodic payments where each payment receives compound interest. One example of an annuity is a Christmas
More informationFilename: P4P 016 Todd: Kim: Todd: Kim:
Filename: P4P 016 Todd: [0:00:18] Hey everybody, welcome to another edition of The Prosperity Podcast, this is No BS Money Guy Todd Strobel. Once again, we have my cohost, bestselling financial author
More informationHow to Overcome the Top Ten Objections in Credit Card Processing
How to Overcome the Top Ten Objections in Credit Card Processing Section #1: Handling the Red Flags Just Fax Your Rates Response: I ll be happy to do that, but until we know if this is truly a fit for
More informationThe following is an article from a Marlboro, Massachusetts newspaper.
319 CHAPTER 4 Personal Finance The following is an article from a Marlboro, Massachusetts newspaper. NEWSPAPER ARTICLE 4.1: LET S TEACH FINANCIAL LITERACY STEPHEN LEDUC WED JAN 16, 2008 Boston  Last week
More informationMike: Alright welcome to episode three of Server Talk, I m here with Alexey. I m Mike. Alexey, how are things been going, man?
Mike: Alright welcome to episode three of Server Talk, I m here with Alexey. I m Mike. Alexey, how are things been going, man? Alexey: They re doing pretty good. Yeah, I don t know, we ve launched two
More informationAudience: Audience: Tim Sain: Audience:
My name is Tim Sain, and you guys are in a budgeting workshop. Has anyone ever done any kind of financial literacy? No. Budgeting? Workshop? Talked about money? Has anybody ever showed you how to spend
More informationChecks and Balances TV: America s #1 Source for Balanced Financial Advice
THE TRUTH ABOUT FIXED RATE ANNUITIES Annuities are like magnets. Most people seem to be either attracted to them, or repelled. As you sit down to read this, where do you stand? In my experience, it s rare
More informationCHAPTER 1. Compound Interest
CHAPTER 1 Compound Interest 1. Compound Interest The simplest example of interest is a loan agreement two children might make: I will lend you a dollar, but every day you keep it, you owe me one more penny.
More informationThe Basics of Interest Theory
Contents Preface 3 The Basics of Interest Theory 9 1 The Meaning of Interest................................... 10 2 Accumulation and Amount Functions............................ 14 3 Effective Interest
More informationHow to Overcome the Top Ten Objections in Credit Card Processing
How to Overcome the Top Ten Objections in Credit Card Processing Handling the Top Ten Objections Objection #1 I have a contract That s exactly why I m calling you, you see most people we work with have
More informationProspecting Scripts. 2 keys to success in Real Estate
Prospecting Scripts 2 keys to success in Real Estate 1. TALK TO PEOPLE 2. ASK THE RIGHT QUESTIONS 1. Doorknocking or cold calling properties around a new listing (inviting them to a property preview)
More informationKim: Thank you Todd, I m delighted to be here today and totally looking forward to our conversation.
Filename: P4P 019 The Facts of Life Insurance Todd: [0:00:18] Hey everybody, welcome to another edition of The Prosperity Podcast, this is No BS Money Guy Todd Strobel. Once again, we re lucky enough to
More informationRealistic Job Preview Youth Counselor (YC)
Realistic Job Preview Youth Counselor (YC) Penny Sampson, Director: Welcome, and thank you for your interest in the position of Youth Counselor at the Sununu Youth Services Center. I am Penny Sampson,
More information3 + 7 1 2. 6 2 + 1. 7 0. 1 200 and 30 100 100 10 10 10. Maths in School. Addition in School. by Kate Robinson
1 2. 6 2 + 1. 7 0 10 3 + 7 1 4. 3 2 1 231 200 and 30 100 100 10 10 10 Maths in School Addition in School by Kate Robinson 2 Addition in School Contents Introduction p.3 Adding in everyday life p.3 Coat
More informationTodd: Kim: Todd: Kim: Todd: Kim:
Todd: [0:00:18] Hey everybody, welcome to another edition of The Prosperity Podcast, this is No BS Money Guy Todd Strobel. Once again, we have my cohost, bestselling financial author Kim Butler with us,
More informationInterest Rates: Loans, Credit Cards, and Annuties. Interest Rates: Loans, Credit Cards, and Annuties 1/43
Interest Rates: Loans, Credit Cards, and Annuties Interest Rates: Loans, Credit Cards, and Annuties 1/43 Last Time Last time we discussed compound interest and saw that money can grow very large given
More informationSeven Things You Must Know Before Hiring a Real Estate Agent
Seven Things You Must Know Before Hiring a Real Estate Agent 1 Introduction Selling a home can be one of the most stressful situations of your life. Whether you re upsizing, downsizing, moving across the
More informationTHE OPTIMIZER HANDBOOK:
THE OPTIMIZER HANDBOOK: LEAD SCORING Section 1: What is Lead Scoring? Picture this: you re selling vehicles, and you have a list that features over two hundred different leads, but you re only allowed
More information>> My name is Danielle Anguiano and I am a tutor of the Writing Center which is just outside these doors within the Student Learning Center.
>> My name is Danielle Anguiano and I am a tutor of the Writing Center which is just outside these doors within the Student Learning Center. Have any of you been to the Writing Center before? A couple
More informationInterest Rates: Credit Cards and Annuities. Interest Rates: Credit Cards and Annuities 1/24
Interest Rates: Credit Cards and Annuities Interest Rates: Credit Cards and Annuities 1/24 Last Time Last time we discussed loans and saw how big an effect interest rates were on a loan, especially a home
More information7 Secrets To Websites That Sell. By Alex Nelson
7 Secrets To Websites That Sell By Alex Nelson Website Secret #1 Create a Direct Response Website Did you know there are two different types of websites? It s true. There are branding websites and there
More informationKeyword Research: Exactly what cash buyers, motivated sellers, and private lenders are looking for online. (and how to get in front of them)
Keyword Research: Exactly what cash buyers, motivated sellers, and private lenders are looking for online. (and how to get in front of them) 52 Keywords + How To Guide More Traffic. More Leads. Keywords
More informationSeven Things You Must Know Before Hiring a Real Estate Agent
Seven Things You Must Know Before Hiring a Real Estate Agent Seven Things To Know Before Hiring a Real Estate Agent Copyright All Rights Reserved 1 Introduction Selling a home can be one of the most stressful
More informationTime Value of Money Dallas Brozik, Marshall University
Time Value of Money Dallas Brozik, Marshall University There are few times in any discipline when one topic is so important that it is absolutely fundamental in the understanding of the discipline. The
More informationMath Matters: Why Do I Need To Know This? 1 Consumer mathematics Paying off credit card debt
Math Matters: Why Do I Need To Know This? Bruce Kessler, Department of Mathematics Western Kentucky University Episode Ten 1 Consumer mathematics Paying off credit card debt Objective: To show how a better
More informationWould You Like To Earn $1000 s With The Click Of A Button?
Would You Like To Earn $1000 s With The Click Of A Button? (Follow these easy step by step instructions and you will) This Version of the ebook is for all countries other than the USA. If you need the
More informationEntrepreneur s M&A Journal Episode 25
Entrepreneur s M&A Journal Episode 25 Intro: Welcome to Entrepreneur s M&A Journal, with lawyer and Harvard MBA Jim Cumbee, a weekly podcast dedicated to helping entrepreneurs make better decisions when
More informationWhat Lawyers Don t Tell You The Realities of Record Keeping
What Lawyers Don t Tell You The Realities of Record Keeping Welcome to the Power of Attorney Podcast which is part of our Conversations that Matter Podcasts. My name is Mary Bart, Chair of Caregiving Matters.
More informationA: We really embarrassed ourselves last night at that business function.
Dialog: VIP LESSON 049  Future of Business A: We really embarrassed ourselves last night at that business function. B: What are you talking about? A: We didn't even have business cards to hand out. We
More informationDate. Hello, Good Afternoon and Welcome to Pegasus Racing! I cordially invite you to join me...
"I m One Of The UK s Top Horse Racing Tipsters & I m Going To Show You My Closely Guarded Secrets Of How I Make Thousands From Horse Racing So You Can Too!" Date Hello, Good Afternoon and Welcome to Pegasus
More informationBOARD OF MANUFACTURED HOUSING Fully Transcribed Teleconference Meeting Minutes. The meeting was called to order by Chairman Ross Wait, at 1:00 p.m.
BOARD OF MANUFACTURED HOUSING Fully Transcribed Teleconference Meeting Minutes TIME: 1:00 P.M. DATE: November 6th, 2008 PLACE: By Telephone Department of Fire, Building and Life Safety 1110 West Washington
More informationIN A SMALL PART OF THE CITY WEST OF
p T h e L a s t L e a f IN A SMALL PART OF THE CITY WEST OF Washington Square, the streets have gone wild. They turn in different directions. They are broken into small pieces called places. One street
More informationEquity Value, Enterprise Value & Valuation Multiples: Why You Add and Subtract Different Items When Calculating Enterprise Value
Equity Value, Enterprise Value & Valuation Multiples: Why You Add and Subtract Different Items When Calculating Enterprise Value Hello and welcome to our next tutorial video here. In this lesson we're
More informationMONEY BOX LIVE. TRANSMISSION: 23 rd APRIL 2007 3.003.30 RADIO 4
THIS TRANSCRIPT IS ISSUED ON THE UNDERSTANDING THAT IT IS TAKEN FROM A LIVE PROGRAMME AS IT WAS BROADCAST. THE NATURE OF LIVE BROADCASTING MEANS THAT NEITHER THE BBC NOR THE PARTICIPANTS IN THE PROGRAMME
More informationC. Retirement Plans a. 401(k) and 403(b)
MODULE 3: SAVINGS/ SPENDING PLAN 33: Start Investing Cast List Darryl Terri Drew Murphy, 4550 years old, white male Alicia Bianca, 4050 years old, white female Synopsis Darryl and Terri discuss investment
More informationHow to Study Mathematics Written by Paul Dawkins
How to Study Mathematics Written by Paul Dawkins Before I get into the tips for how to study math let me first say that everyone studies differently and there is no one right way to study for a math class.
More informationFactual statements in this course are made as of the date the course was created and are subject to change without notice.
1 HOW TO AVOID CHOPPY MARKETS Dr. Barry Burns Copyright 2007 Top Dog Trading IMPORTANTREAD CAREFULLY: Reproduction, translation, or distribution in any form or by any means, or storage in a data base
More informationPolynomials and Factoring. Unit Lesson Plan
Polynomials and Factoring Unit Lesson Plan By: David Harris University of North Carolina Chapel Hill Math 410 Dr. Thomas, M D. 2 Abstract This paper will discuss, and give, lesson plans for all the topics
More information6 Steps To Success With Your Web Agent Solutions Website
6 Steps To Success With Your Web Agent Solutions Website By Jay Kinder and Michael Reese Introduction Congratulations on your decision to join the Web Agent Solutions family. It s an enormously effective
More informationFractions and Decimals
Fractions and Decimals Tom Davis tomrdavis@earthlink.net http://www.geometer.org/mathcircles December 1, 2005 1 Introduction If you divide 1 by 81, you will find that 1/81 =.012345679012345679... The first
More informationCREATE TAX ADVANTAGED RETIREMENT INCOME YOU CAN T OUTLIVE. create tax advantaged retirement income you can t outlive
create tax advantaged retirement income you can t outlive 1 Table Of Contents Insurance Companies Don t Just Sell Insurance... 4 Life Insurance Investing... 5 Guarantees... 7 Tax Strategy How to Get TaxFree
More informationUNIT AUTHOR: Elizabeth Hume, Colonial Heights High School, Colonial Heights City Schools
Money & Finance I. UNIT OVERVIEW & PURPOSE: The purpose of this unit is for students to learn how savings accounts, annuities, loans, and credit cards work. All students need a basic understanding of how
More informationNEW DRIVERS HOW TO TAKE THE ONTHEROAD SKILLS TEST. KELLY MANNING: Welcome to DMV Infocast, an audio production of the
NEW DRIVERS HOW TO TAKE THE ONTHEROAD SKILLS TEST KELLY MANNING: Welcome to DMV Infocast, an audio production of the Connecticut Department of Motor Vehicles. This is Kelly Manning, Infocast Editor.
More informationSales Lead Brokerage Profit Plan Bonus Document
Sales Lead Brokerage Profit Plan Bonus Document Introduction Hello and thanks for ordering the Sales Lead Brokerage Profit Plan through the Money Makers Reviewed website. As you ll know if you read my
More informationThree Attributes of Every Successful Merchant Services Program20140604 16021
Three Attributes of Every Successful Merchant Services Program20140604 16021 [Start of recorded material] [Starts Mid Sentence] thank everyone that s joined the call today. I know everybody is busy with
More informationChapter 2. My Early Days Trading Forex
Chapter 2 My Early Days Trading Forex I want to talk about my early days as a Forex trader because I m hoping that my story will be something you can relate to. So it doesn t really matter if you are brand
More informationHow to Outsource Without Being a Ninnyhammer
How to Outsource Without Being a Ninnyhammer 5 mistakes people make when outsourcing for profit By Jason Fladlien 2 Introduction The way everyone does outsourcing is patently wrong, and this report is
More informationDeciding Which Bills to Pay First Lunch & Learn  Lesson 5 Presented by Nancy Porter
Deciding Which Bills to Pay First Lunch & Learn  Lesson 5 Presented by Nancy Porter Welcome again. This week we are going to talk about deciding which bills to pay first. I m glad Deborah gave you a little
More informationWarm Market Scripts Ideas.
WarmMarket ScriptIdeas Warm Market Scripts Ideas. Schedule a time to talk with them soon after they get the information. Followup is the key to success. See some ideas. Speak to your upline support and
More informationWhatever s special about your family life, make sure you protect it
Whatever s special about your family life, make sure you protect it Your family is special, so make sure you protect it When something awful happens, it feels like normal life stops. But, even for a family
More informationBLOSSOMS MODULE ARE RANDOM TRIANGLES ACUTE OR OBTUSE? By Gilbert Strang Professor of Mathematics Massachusetts Institute of Technology
BLOSSOMS MODULE ARE RANDOM TRIANGLES ACUTE OR OBTUSE? By Gilbert Strang Professor of Mathematics Massachusetts Institute of Technology Hi! I m Gilbert Strang. I teach math at MIT. Mostly what I teach is
More informationSteps to Proving a Theorem
Steps to Proving a Theorem Step 1: Understand Goal What am I looking for? What should the last sentence in my proof say? What are some equivalent ways to state what I want? Are there any complicated definitions
More informationRandom Fibonaccitype Sequences in Online Gambling
Random Fibonaccitype Sequences in Online Gambling Adam Biello, CJ Cacciatore, Logan Thomas Department of Mathematics CSUMS Advisor: Alfa Heryudono Department of Mathematics University of Massachusetts
More informationCHAPTER 5. Interest Rates. Chapter Synopsis
CHAPTER 5 Interest Rates Chapter Synopsis 5.1 Interest Rate Quotes and Adjustments Interest rates can compound more than once per year, such as monthly or semiannually. An annual percentage rate (APR)
More informationArticle for Construction Business Owner magazine, 2011 (series of three articles)
Article for Construction Business Owner magazine, 2011 (series of three articles) Series Title: Creating a Culture of Employees Who Think and Act Like Owners Article One Title: The Importance of Educating
More informationAnytime Adviser Checking Account Coach
Anytime Adviser Checking Account Coach Welcome. This interactive guide coaches you in managing your checking account. You may move from chapter to chapter by selecting headings from the left. Click on
More informationCHAPTER 5 INTRODUCTION TO VALUATION: THE TIME VALUE OF MONEY
CHAPTER 5 INTRODUCTION TO VALUATION: THE TIME VALUE OF MONEY Answers to Concepts Review and Critical Thinking Questions 1. The four parts are the present value (PV), the future value (FV), the discount
More informationZCorum s Ask a Broadband Expert Series:
s Ask a Broadband Expert Series: The Advantages of Network Virtualization An Interview with Peter Olivia, Director of Systems Engineering ZCorum 1.800.909.9441 4501 North Point Parkway, Suite 125 Alpharetta,
More informationConnectedness and the Emotional Bank Account
Connectedness and the Emotional Bank Account Directions This is a selfguided activity that can be completed by parents, teens or both. It contains five parts and should take about 45 minutes to complete.
More informationONE DOLLAR AND EIGHTYSEVEN CENTS.
T h e G i f t o f t h e M a g i p T h e G i f t o f t h e M a g i ONE DOLLAR AND EIGHTYSEVEN CENTS. That was all. She had put it aside, one cent and then another and then another, in her careful buying
More informationLIFE INSURANCE STRATEGY GUIDE
LIFE INSURANCE 101 STRATEGY GUIDE : STRATEGY GUIDE TABLE OF CONTENTS Why You May Need Life Insurance... 5 Shopping for Life Insurance... 5 How Much Life Insurance to Obtain... 6 Calculating Total Funds
More informationCIO 24/7 Podcast No.6 Cloud Computing
CIO 24/7 Podcast No.6 Cloud Computing Welcome to edition six of Accenture s CIO 24/7 podcast. We bring you practical real world insight on IT delivery and strategy straight from the leaders of Accenture
More informationPlanning for Your Retirement
STUDENT MODULE 6.1 RETIREMENT PLANNING PAGE 1 Standard 6: The student will explain and evaluate the importance of planning for retirement. Planning for Your Retirement Lindzi and Lezli will attend retirement
More informationThank you so much for having me. I m really excited to be here today.
Welcome to The Boomer Business Owner. My guest today is Ty Crandall. Ty is an honorary Baby Boomer, internationally known speaker, author, and business credit expert. With over 16 years of financial experience,
More informationFinancial Freedom: Three Steps to Creating and Enjoying the Wealth You Deserve
Financial Freedom: Three Steps to Creating and Enjoying the Wealth You Deserve What does financial freedom mean to you? Does it mean freedom from having to work, yet still being able to enjoy life without
More information0:00:18 Todd: 0:00:30 Kim: 0:01:15 Todd: 0:02:10 Kim: 0:04:10 Todd:
0:00:18 Todd: Hey everybody, welcome to another edition of The Prosperity Podcast, this is No BS Money Guy Todd Strobel. Once again, we have my cohost and bestselling financial author Kim Butler with us,
More information100 40 5 4 = 149. how many left? what s the difference? 5 60 80 4 = 149. take away. Maths in School. minus. Subtraction in School.
100 40 5 4 = 149 0 635 735 775 780 784 1000 8 5 2 1 5 3 how many left? what s the difference? 5 60 80 4 = 149 take away 0 635 640 700 780 784 1000 Maths in School minus Subtraction in School by Kate Robinson
More information7 Financial Talks to Have With Your Kids Before They Start College
Publication: The Credit Solution Program Date: August 16, 2014 Author: Aaron Crowe 7 Financial Talks to Have With Your Kids Before They Start College Before your children start college, it s a good idea
More informationsession 4the cost of your life
session 4the cost of your life Objective This session is designed to get youth thinking about what the life they want is going to cost when they move out on their own. For example: Have them consider
More informationSpecial Report: 5 Mistakes Homeowners Make When Selling A House. And The Simple Tricks To Avoid Them!
Special Report: 5 Mistakes Homeowners Make When Selling A House And The Simple Tricks To Avoid Them! 1 Special Report: 5 Mistakes Homeowners Make When Selling A House Dear Homeowner, And The Simple Tricks
More informationGood Fast or Low cost marketing
Email Marketing 101 Good Fast or Low cost marketing We ve all heard the old adage about how, when it comes to marketing, you can get what you need done well, delivered quickly or produced inexpensively;
More information9.2 Summation Notation
9. Summation Notation 66 9. Summation Notation In the previous section, we introduced sequences and now we shall present notation and theorems concerning the sum of terms of a sequence. We begin with a
More informationMammon and the Archer
O. H e n r y p Mammon and the Archer OLD ANTHONY ROCKWALL, WHO HAD MADE millions of dollars by making and selling Rockwall s soap, stood at a window of his large Fifth Avenue house. He was looking out
More informationRevised Version of Chapter 23. We learned long ago how to solve linear congruences. ax c (mod m)
Chapter 23 Squares Modulo p Revised Version of Chapter 23 We learned long ago how to solve linear congruences ax c (mod m) (see Chapter 8). It s now time to take the plunge and move on to quadratic equations.
More informationIncome For Life Introduction
Income For Life Introduction If you are like most Americans, you ve worked hard your entire life to create a standard of living for yourself that you wish to maintain for years to come. You have probably
More informationDatabase Management System Prof. D. Janakiram Department of Computer Science & Engineering Indian Institute of Technology, Madras Lecture No.
Database Management System Prof. D. Janakiram Department of Computer Science & Engineering Indian Institute of Technology, Madras Lecture No. 23 Concurrency Control Part 4 In the last lecture, we have
More informationBETTER YOUR CREDIT PROFILE
BETTER YOUR CREDIT PROFILE Introduction What there is to your ITC that makes it so important to you and to everyone that needs to give you money. Your credit record shows the way you have been paying your
More information0.7 Quadratic Equations
0.7 Quadratic Equations 8 0.7 Quadratic Equations In Section 0..1, we reviewed how to solve basic nonlinear equations by factoring. The astute reader should have noticed that all of the equations in that
More informationThe One Key Thing You Need to Be Successful In Prospecting and In Sales
The One Key Thing You Need to Be Successful In Prospecting and In Sales The secret key to being successful in prospecting and in sales found in this report will work in ANY INDUSTRY for any product or
More informationKeys to Retirement Planning and Investing
Keys to Retirement Planning and Investing Table of Contents Keys to Retirement Planning Keys to Investing for Retirement 1 2 3 4 5 Find out how much you ll need for retirement. Most experts agree that
More informationA Learning Paths Whitepaper. Rapid Onboarding 3 Keys to Success
A Learning Paths Whitepaper Rapid Onboarding 3 Keys to Success The Importance of Rapid Onboarding How soon would you be confident assigning a new employee to work with your most valued customer? When do
More informationReal Estate Investing Podcast Episode # 74 The ABCs of Finding and Training a Virtual Assistant Hosted by: Joe McCall and Alex Joungblood
Real Estate Investing Podcast Episode # 74 The ABCs of Finding and Training a Virtual Assistant Hosted by: Joe McCall and Alex Joungblood Jesse: Hey, welcome back. This is Real Estate Investing Mastery.
More informationWhat did I learn from participating in the career fair, and how did my presentation contribute to my classmates knowledge?
Career Fair Reflection 10 CAREERS The BIG Idea What did I learn from participating in the career fair, and how did my presentation contribute to my classmates knowledge? AGENDA Approx. 45 minutes I. Warm
More information