0:00

We are just doing future value of annuities, and I'll show you, now,

Â why this is such a cool thing, and what I'm going to do is I'm going to do

Â two examples, both for future value of an annuity, and what's the other thing we do?

Â Present value of an annuity, and remember,

Â annuities, the amount of the annuity when you write,

Â could be called C, but when you go to calculator, or a spreadsheet,

Â we'll call it BMT, because that's what they call it, right, makes sense.

Â Okay, I would like you to stare at this problem.

Â 0:36

And I know you have the ability to pause and so on.

Â But I like to pause video, and what I'm going to do for every example, and

Â if I don't you should do this, is I'm going to read out the problem for

Â you and we'll talk about it a little bit, and

Â then I would really encourage you to try to do the problem.

Â 0:59

I'll do it with you, but

Â I would encourage you to kind of think actively and be participating in it.

Â because I can't see whether you're doing it or not, but I hope you do, okay.

Â So what will be the value of your portfolio, what is a portfolio?

Â Portfolio and there's lingo in finance, portfolio means

Â whatever your investment is, wherever you put your money.

Â So the word portfolio is used generically,

Â because you'll see later it's a hangover from the fact that life has risk,

Â and if life has risk and you do not like risk,

Â which most people don't, you tend to not put all your eggs in one basket.

Â So, the fact that you hold a basket of different things is called a portfolio.

Â Okay? I've tried to emphasize

Â words which I take for granted.

Â Because if you're new to finance, which most of you probably are,

Â You need to understand why certain language is used very commonly.

Â After retirement, if you deposit $10,000 every year in a pension fund.

Â Now if you're really young, say you're 15 and taking this class,

Â which I hope some of you are, don't worry too much about retirement.

Â Have some fun.

Â You're in high school.

Â You haven't even begun earning, hopefully, just having fun.

Â So, but this is something that you will do at some point, most people do.

Â So what I recommend is just think of it as an intellectual problem, but actually,

Â it's a very real problem.

Â So what will be the value of your portfolio at retirement if

Â you deposit $10,000 every year in a pension fund?

Â 2:47

What is a pension fund?

Â A pension fund is a place or

Â an account which hopefully has multiple assets if you're risk averse,

Â multiple kinds of investments, a bond, a stock and we'll talk about those.

Â You put $10,000 every year.

Â Why 10,000 fixed amount?

Â Well, nothing is forcing you to put 10,000 every year.

Â It can be 11,000 one year, 9,000 the other, but

Â oddly enough, to make life simple perhaps, many people tend to

Â put away a certain amount of money every year for things they need in the future.

Â So the notion of a pension fund is,

Â at some point I'm going to retire and I need some money.

Â So you put away 10,000 every year.

Â You plan to retire in about 40 years and expect to earn 8% on your portfolio.

Â So, what have I given you?

Â I've given you everything you need.

Â I've given you PMT or C, which is 10,000.

Â I've given you the number of years left for you to retire,

Â 40, and I've given you an interest rate that

Â you're likely to earn on your portfolio, which means where you put your money.

Â A bank, whatever, we'll talk about that in a second, but

Â let's just focus on this and try to do this problem.

Â I hope you have been listening to me, and I hope you've been paying attention

Â because if you pay attention to a problem, it gets to be a little intense,

Â and I'll do the problems with you and I have promised myself today I will spend

Â a lot of time just doing problems with you because that's how you learn.

Â And another piece of advice, I've given you textbooks to read, that you can go

Â 4:38

get and read, and they can be secondhand, they can be whatever.

Â The fundamental principles of finance have been known since we were in the cave.

Â So just remember that what you are trying to do is focus on the fundamentals.

Â So read whatever you want if the video doesn't satisfy your curiosity,

Â but the video is trying to be self-sufficient.

Â So let's do this, let's now start doing the problem, and

Â what I'm going to do is I'm going to do two problems for future value,

Â two problems for present value, but I'll take breaks with you.

Â So I'll let you know that maybe it's time to take some time off, get some coffee.

Â Go jog around the apartment building where you live,

Â or talk to your friend, or watch a video on YouTube, why not?

Â Okay, so let's get started.

Â 5:55

If you remember that or if you recognize that,

Â you'll be okay, so how many points in time?

Â 41.

Â 0, 1 through 40.

Â How many periods of time?

Â Well, it takes two points of time to make a period, so there's one less.

Â One, two.

Â So what we'll do to make our life simple is we'll assume that

Â the first $10,000 is at the end of the year.

Â Why did I do that?

Â I could always start saving at this point, but

Â I'm doing it simply so that I can use the formula just directly.

Â Use the calculator and do it and set up.

Â We can change that so don't worry.

Â You can start a payment today and change it.

Â It's just a minor difference.

Â How much?

Â 6:46

Another thing that seems a little bit odd or

Â manufactured in this formula Is that you're saving at year 42.

Â Right, you may not be, right?

Â Or actually you messed up saving in between, but for convenience we

Â are trying to understand the problem, which has got 40 of these guys.

Â 7:11

So the good news is, even though this formula is very complicated,

Â right, you divide this by how much?

Â You carry it forward by how much?

Â One period, but there's no money.

Â How much do you carry this forward by?

Â 39 periods.

Â How much do you carry this forward by?

Â 38.

Â Which is the simplest piece of this, this guy.

Â Why?

Â Because I'm asking you what is the future value at this point in time?

Â 7:43

All right?

Â So the future value of this point in time of this guy is just itself.

Â That's what I mean.

Â If you learn how to travel in time.

Â If you're at 40, and you are, imagine you are at point number 40.

Â The last PMT or C is $10,000, so at time 40, it's exactly 10.

Â But when you look back, if you were to,

Â you have to carry the past amounts you've invested as earning money.

Â Which is good news for you, right?

Â And it's earning how much?

Â 8%, and let me tell you, that's not bad at all, right?

Â And, we'll talk about that when we talk about risk and return, in a second.

Â So, do you understand the nature of the beast?

Â The beast is not easy.

Â It's not easy.

Â It's like doing 39 future values and adding them up, right?

Â So, what I'm going to do is, I'm going to now shift to using a calculator.

Â Okay.

Â 8:59

And I'm going to use the formula of pmt.

Â Remember, whatever you don't know, you type in here.

Â So, did I, yeah, pmt.

Â Right?

Â And, the one thing you have to do before you do pmt,

Â and not get excited like me, I'm Mr. Hyper, you have to put equal signs,

Â so that, otherwise you'll get all kinds of garbage.

Â 9:27

Okay, you open it up.

Â What is the first number that shows up?

Â The first number that shows up is the rate of return.

Â And we know how much are we earning.

Â We're earning .08.

Â Again, emphasizing this, the only reason I'm using Excel right now, is what?

Â Simply, because the calculation is very difficult.

Â But, I've explained to you what's going on.

Â You're doing 40 carry forwards, but actually only 39, because the first one

Â 9:59

is 0, and the last one is just itself.

Â So that's why, I said it, okay?

Â So you put a comma, and what's the next one?

Â 40, number of periods.

Â Right?

Â And Actually,

Â let me just backtrack a little bit.

Â The thing that we want to figure out is fv.

Â So put in fv, and now I want rate, .08.

Â You see, what I was doing, we'll do next time.

Â [LAUGH] So, number of periods is 40, and in this case,

Â I know my pmt, and my pmt is $10,000.

Â Right?

Â And what is pv?

Â Don't worry about it.

Â It's not in there.

Â Just hit, okay, so what do you get?

Â And if, you get a lot of money, basically.

Â You get $2,000,000, $2,590,000,

Â right, it's 2,590,565.

Â So, what does this tell you?

Â This tells you that, if you invest $10,000 in a bank 40 times,

Â the future value of that will end up being 2.59 million dollars.

Â So, what I'm going to do, I'm going to try to talk you through the problem again.

Â 11:34

I calculated future value.

Â So in order to calculate future value of something that I don't know,

Â I have to use the future value function in the calculator or in the spreadsheet.

Â And out popped, I gave this information,

Â $10,000 was pmt.

Â 40 was m.

Â But most importantly, 8% was r.

Â So, I gave all of this information to Excel or a calculator, whatever

Â you choose to be using, simply because it's a very complicated calculation.

Â Conceptually, it's not that difficult.

Â And we got 2.59 mil.

Â 12:28

And I'm going to just use it approximately,

Â because I'm not going to calculate and write all the digits and so on.

Â So what has happened here?

Â Let me just walk you through this problem.

Â First of all, remember yesterday whenever I asked you,

Â what is the answer to a finance question or anybody asked you, what should you say?

Â Compounding, but you always have to pause because you want to look smart, right?

Â So you take a pause and you say compounding into it.

Â So let me ask you the following question.

Â Suppose there was no interest rate.

Â 13:05

Or in other words, how much of the $10,000 are you throwing in?

Â And suppose interest is 0, this problem is very simple to do, why?

Â Because you do 40 times 10,000, you have $400,000, right?

Â So the interest rate time value money is 0, you will have a lot of money

Â in your bank account, but how much will it be?

Â $400,000.

Â How much do you have if the interest rate is 8%,

Â $2.59 million,

Â huge difference in magnitude, and who's the culprit?

Â Compounding.

Â 13:47

In this case the culprit is helping you, but

Â in the case of, if you are paying it, it hurts.

Â So we'll do a loan later.

Â So here it's helping you.

Â So let's talk through this problem a little bit and so

Â that you understand how empowered you are.

Â 14:36

But I would encourage you to think about what your needs are in the future, so

Â that you can figure out how much you need to put away.

Â And we'll do a problem quite the reverse in a second.

Â So you put away $10,000.

Â Who decides that?

Â You decide that. Second question,

Â what is the other number in this problem?

Â It's 40.

Â How many years to retirement.

Â I know you can say that your job may have a retirement age or so

Â and so forth, but I challenge you on that.

Â 15:14

By that, I mean, you should keep learning in life, so

Â you always have the opportunity to do something, right?

Â And we are talking about a money problem, but It could be about anything.

Â So let's take the extreme case scenario.

Â You're doing a regular job and you know 40 years from now you're going to retire.

Â My point there is, you have more control on that, but sometimes people don't.

Â People have jobs, where they are dependent on the employer,

Â 15:44

on how many years they work.

Â But it's a given.

Â I mean you won't go to a financial advisor and say, in how many years do I retire?

Â The person will give you an answer, but

Â [LAUGH] he'll charge you a lot of money for giving that, right?

Â So the fact is also information that you should know.

Â 10,000 is the information you should know.

Â Now the 8%.

Â I'm going to violate the assumption that I said make it the back of your mind,

Â but to be fair I never said assume it's not there.

Â I said I know it's there.

Â Keep it at the back of your mind, but for the convenience sake we'll ignore it, and

Â that is risk.

Â 16:36

If anybody knew what the interest rate was in the future for

Â the next 40 years or something they would be omnipresent.

Â They would know the future.

Â We all wanted to be like that, but I think the beauty of life is nobody knows, and

Â in fact one of the most profound developments in finance in recent years,

Â I shouldn't say recent.

Â Say last 40, 50 years, which gets challenged because it's a good idea.

Â Bad ideas don't get challenged, right?

Â Good ideas get challenged.

Â So the notion there is that nobody in a good market should be able to tell

Â the future because everything we know is already in the marketplace, right?

Â That's why I said competitive markets at the beginning are extremely important to

Â what we do.

Â So quick question.

Â Who determines the 8%, and the answer is you,

Â and this is where I like to bring in risk a little bit.

Â Why? Because 8%,

Â let me tell you if you get over the next 40 years may the force be with you.

Â [LAUGH] Because it's not going to be easy.

Â You have to take risk to get high rates of return, and with risk comes volatility.

Â So the 8% the higher return the more likely it is that

Â you are jumping all over the place like the stock market.

Â So, if you want to be safer what will you have to do?

Â You will have to lower the interest rate to say 4%.

Â Put it in a bond issued by the government in the long run and

Â you'll be safer, but what will happen to the 2.59 million?

Â Do this exercise for yourself?

Â Let's after this class is over use 4% instead of 8%, and what will you see.

Â A dramatic drop in the amount of money you have at the end.

Â So why am I emphasizing so much in one little problem?

Â Because that's what finance's beauty is.

Â 18:31

If you understand these problems inside out and

Â you know how to use the excel spreadsheet to calculate the answers you've arrived.

Â So if you use 4% what happens?

Â You kind of get rid of your nervousness about risk,

Â but what happens to the amount of money you have?

Â It'll drop dramatically, right?

Â We know that.

Â We know the power of compounding.

Â It helps when interest rates go up, it hurts when it goes down.

Â 18:59

So, having said that if the interest rate is 4% you're going to suffer.

Â What can you say about the 8%, 4% choice?

Â Neither one is good or bad.

Â Neither one is good or bad.

Â What's important is you have control over the the 4 and

Â the 8 in the following sense.

Â Not that you can predict it, but if you choose to put 4% in your calculations.

Â It has to be matched by your investment strategy.

Â So if you're thinking you're going to earn 8% and put it in the bank,

Â especially today, and if this low interest rates go on you're dreaming.

Â You'll have closer to $400,000 if the bank is still there after 40 years, right?

Â So think like that.

Â Everything is under your control, and the beauty of market says for

Â most of us we do not need to second guess what the interest rates are.

Â All we need to do is match our preferences of risk with our investment strategy,

Â and then not worry about it too much.

Â