0:00

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

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

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

Present value of an annuity, and remember,

annuities, the amount of the annuity when you write,

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

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

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

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

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

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

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

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

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I'll do it with you, but

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

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

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

Portfolio and there's lingo in finance, portfolio means

whatever your investment is, wherever you put your money.

So the word portfolio is used generically,

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

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

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

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

Okay? I've tried to emphasize

words which I take for granted.

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

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

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

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

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

Have some fun.

You're in high school.

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

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

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

it's a very real problem.

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

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

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What is a pension fund?

A pension fund is a place or

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

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

You put $10,000 every year.

Why 10,000 fixed amount?

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

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

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

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

So the notion of a pension fund is,

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

So you put away 10,000 every year.

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

So, what have I given you?

I've given you everything you need.

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

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

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

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

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

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

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

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

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

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

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

4:38

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

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

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

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

but the video is trying to be self-sufficient.

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

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

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

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

Go jog around the apartment building where you live,

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

Okay, so let's get started.

5:55

If you remember that or if you recognize that,

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

41.

0, 1 through 40.

How many periods of time?

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

One, two.

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

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

Why did I do that?

I could always start saving at this point, but

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

Use the calculator and do it and set up.

We can change that so don't worry.

You can start a payment today and change it.

It's just a minor difference.

How much?

6:46

Another thing that seems a little bit odd or

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

Right, you may not be, right?

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

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

7:11

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

right, you divide this by how much?

You carry it forward by how much?

One period, but there's no money.

How much do you carry this forward by?

39 periods.

How much do you carry this forward by?

38.

Which is the simplest piece of this, this guy.

Why?

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

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All right?

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

That's what I mean.

If you learn how to travel in time.

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

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

But when you look back, if you were to,

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

Which is good news for you, right?

And it's earning how much?

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

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

So, do you understand the nature of the beast?

The beast is not easy.

It's not easy.

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

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

Okay.

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

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

So, did I, yeah, pmt.

Right?

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

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

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

9:27

Okay, you open it up.

What is the first number that shows up?

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

And we know how much are we earning.

We're earning .08.

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

Simply, because the calculation is very difficult.

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

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

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is 0, and the last one is just itself.

So that's why, I said it, okay?

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

40, number of periods.

Right?

And Actually,

let me just backtrack a little bit.

The thing that we want to figure out is fv.

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

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

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

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

Right?

And what is pv?

Don't worry about it.

It's not in there.

Just hit, okay, so what do you get?

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

You get $2,000,000, $2,590,000,

right, it's 2,590,565.

So, what does this tell you?

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

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

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

11:34

I calculated future value.

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

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

And out popped, I gave this information,

$10,000 was pmt.

40 was m.

But most importantly, 8% was r.

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

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

Conceptually, it's not that difficult.

And we got 2.59 mil.

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And I'm going to just use it approximately,

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

So what has happened here?

Let me just walk you through this problem.

First of all, remember yesterday whenever I asked you,

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

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

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

So let me ask you the following question.

Suppose there was no interest rate.

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

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

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

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

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

$400,000.

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

$2.59 million,

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

Compounding.

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In this case the culprit is helping you, but

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

So we'll do a loan later.

So here it's helping you.

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

that you understand how empowered you are.

14:36

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

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

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

So you put away $10,000.

Who decides that?

You decide that. Second question,

what is the other number in this problem?

It's 40.

How many years to retirement.

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

and so forth, but I challenge you on that.

15:14

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

you always have the opportunity to do something, right?

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

So let's take the extreme case scenario.

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

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

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

15:44

on how many years they work.

But it's a given.

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

The person will give you an answer, but

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

So the fact is also information that you should know.

10,000 is the information you should know.

Now the 8%.

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

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

I said I know it's there.

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

that is risk.

16:36

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

the next 40 years or something they would be omnipresent.

They would know the future.

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

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

I shouldn't say recent.

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

Bad ideas don't get challenged, right?

Good ideas get challenged.

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

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

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

what we do.

So quick question.

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

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

Why? Because 8%,

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

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

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

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

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

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

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

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

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

Do this exercise for yourself?

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

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

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

Because that's what finance's beauty is.

18:31

If you understand these problems inside out and

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

So if you use 4% what happens?

You kind of get rid of your nervousness about risk,

but what happens to the amount of money you have?

It'll drop dramatically, right?

We know that.

We know the power of compounding.

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

18:59

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

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

Neither one is good or bad.

Neither one is good or bad.

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

the 8 in the following sense.

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

It has to be matched by your investment strategy.

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

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

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

So think like that.

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

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

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

and then not worry about it too much.