0:00

So, I'll give you a minute to read this problem again and

you'll recognize this problem.

And I the reason I'm doing it is because it kind of captured everything we did

last time.

But as you read it, you should see a difference.

So I'm throwing in something new into the problem, so

that you can think creatively to do this problem again.

So the problem again states that you're 30 years old, you believe you will save for

the next 20 years until you're 50.

This is exactly the same as last time for 10 years following

that until you retired at age 60, you have an inability.

Because of your expenses, college expenses, weddings and so on to save.

And remember, you are 30, you are trying to figure your life out in the future and

it's not difficult to do.

This is all for your own thinking, not somebody else telling you what to do.

So I'm kind of empowering you to think for yourself.

1:00

Now at 60, if you want to guarantee yourself

$8,000 per month after that until you quote,

unquote are no more at 80.

How much do you need to save for the next 20 years starting at age 30?

But the one wrinkle I've thrown in is I've made this from an annual

to a monthly problem and I'm going to let that stay up there for a second.

Since we've seen this problem before, I'm creating a new twist and

we shouldn't be able to worry too much about the fact that there's months now.

On the other hand, I think the problem becomes much richer and

much more real world, because of compounding.

And you should always responds for that.

So let's get started and I'm going to, since we are beginning this class,

I'm going to just try to address this issue right away.

So first thing you always do is draw a time line and

I'm borrowing this timeline from last time, but notice I've done something.

And if you're looking at this slide carefully, what you'll notice

is that I have made my life very simple by doing the first thing, which

is under my control is defining a period according to the nature of the beast.

So the problem here says that I'll be saving monthly and

the time line converted to months solves a lot of my problems.

So the question now is between years 30 and

50, there were 20 years, but actually there are 240 months.

Again, between years 60 and 80 there were 20 years?

There are 240 months.

So the question is between 50 and

60 when I'm not able to save, but I'm not dissaving.

How many years of that?

Ten, but recognize that no longer can you work with the errors.

3:39

And as I told you last time, don't look back.

Look forward, because you're making decisions.

And then decide when you look forward, what is it that you're trying to solve?

So here, you want how much per month?

I believe my numbers now are 8,000 per

month you need for a long period of time.

So the PMT input in solving this problem is

8,000 and we'll do it in a second.

M is how much?

M now is not 20 years, it's 240 months.

Basically, this has to match this.

If these two are not aligned, you have a problem.

Most importantly, you are to align this with the problem.

So if an annual interest rate is stated at 8%,

the monthly interest rate should be 0.08/12.

If you were getting compounding on a quarterly basis, it would be different.

Daily basis, it would be different.

So the question here is now, how do I solve this problem and

what will it tell me?

Because we have done this problem before, I'm going to recognize you

remember that the first thing I'll try to do is PV of what I need and

I'm going to put subscript here 60.

So that, it's you see the calculator Excel doesn't know where you are, but you do.

5:15

So you know when you solve this problem,

you're not at 0.30, you're 0.60 in the future.

You're already there in your mind and you're looking forward,

you're not looking back.

Even though you are at 60 and it's yet to come 30 years from now,

when you're solving this piece, you're looking forward.

The same principle.

So let's see.

This is a tough one to do in your head.

As I said, if you do it, there's something wrong with you.

So let's presume you can't do it and let's use Excel to do it.

So what I'm going to do is I'm going to toggle and go to Exce.

So let's see.

And I had problems myself with this class that I would do a lot of execution,

but I'm not doing execution without hopefully, a need for doing it.

So hopefully, this is helpful to you without being hand holding.

So remember, what are we trying to solve for it?

We are trying to solve for a PV problem, even last time.

Remember, I screwed up is I thought I was solving a PMT problem, but

I was actually solving a PV.

So the thing that your solving for is function and its PV.

Remember in your head, it's PV in year six now.

What is the interest rate?

0.08, but you gotta pause.

You do not have annual compounding, you have monthly compounding.

So you divide that by 12.

How many periods do you have?

240.

Don't put 20, because if you put an interest rate of 0.2 divided by 12 and

you put 20, your annual interest rate is almost nonexistent.

Which by the way, matches with reality these days.

But for the time being, [LAUGH] let's do this problem.

So you have 240 pmt and then fv is what?

We don't have a future value here and

you have you got all the numbers in there, 240, yes.

PMT is something I do know.

So the PMT comes before a FV and I press 8,000.

7:27

So what do you get?

You get $956,434 and

I'm going to avoid the cents.

So everybody recognize this?

So, it's pretty straightforward and I'm going to leave it there and

I'm going to toggle back to our presentation.

So now we know, by the way, this is art form.

I'm going between that different media without you even knowing,

I hope you like that.

Anyway, so PV60.

We saw was, and I'm going to

confirm this with my own notes,

956,434.

I'm writing all these details, simply because as I said,

my philosophy is that I will not give you resources unless they

are absolutely necessary for you to then sit back and consume.

I want you to work through these problems yourself, so

I'm giving you some minimal information.

Now the problem is I cannot stay here.

I got to match the tools I have to the problem I can do.

Now clearly, when you become proficient, you can do this on an Excel and

do it all faster and so on.

But let's do it a little bit logically, I want to bring it back here.

Why do I want to do that?

And the reason is,

I do know how to calculate a PMT, which I'm trying to calculate.

What is my saving monthly?

If I know its future value at this point, but if there's a gap, it's a problem.

So why not take the problem to something you know how to do rather than

just wait there and expect some magic to occur and it's not a big deal.

It helps your thinking.

So now what do we do?

Let's go back and try to understand what's going on and

do Excel again and so what I'm going to do now is I'm going to,

as I said before, toggle back to Excel.

Now the good news is I already have a number up there, 956.

So let me take =pv.

Why did I do PV?

Because now, I am bringing something in to your 60 to your 50 to match what I want.

So let's do it.

We have to be a little careful, because I think, as I said, if you're not careful,

you'll but in the wrong numbers.

So now, 0.08/12.

Again, please remember, not 8%, but 12 of that.

How many periods?

Well, between 50 and 60.

There are 10 years, put 120 months.

So we've got those two numbers and now we need to figure out what do I

put in next and remember the next item here is PMT.

That's how it's been set up in Excel, but I don't have a PMT.

This time, I don't.

I put a zero there, but I do have future value.

And the future value is sitting in its cell.

We just solved the problem, I retained that cell A1.

Look what happens.

I think this happened last time too.

Just because you're doing it monthly, it doesn't mean this won't happen.

The value has dropped drastically.

In fact, to less then half and what's the reason for it?

120 months have passed and the monthly interest rate is non-trivial.

So now we are at a point where this again.

Again, let me just toggle back to the PowerPoint.

Now the good news is where am I?

I am now at this point and I have a number that I can deal with,

I think it's 430,896.

430,896.

So what does this number mean?

Let's just pause for a second.

It was more than twice here.

11:40

So what does this number mean in English?

This is the amount of money I should have in my bank at at 50 to support what?

To support all my post retirement 8,000 a month expenses.

So that's one way of thinking about it.

So now, however, I don't have that money.

[LAUGH] So I need to act today, starting end of next month to start saving.

But what kind of a problem is it?

It's a PMT problem.

How much money do I save a month, who's future value I already know?

Make sense?

Let's do it.

Just one more step and then after that, I will take a break,

because I want you to kind of think about this a little bit and see what's going on.

So let's go to Excel.

So now if you look at the two numbers on top, the first number is,

it's showing negative, simply because I'm putting a positive number as a payment.

So now, 430 needs to be in the bank at which time?

At time age 50.

That is 956 it grows into, if it stays in the bank or in a portfolio.

So let's do the PMT problem, because now we're solving for PMT.

How many periods do you need?

First is you need 20 periods, but you also need the rate of return.

Before that, 0.08 divided by 12.

Everybody got that?

How many periods did I save for?

20 years, which is 240 months.

Fair enough?

Got it.

Now the next number and again, you have to just be paying attention,

because as to what Excel offers and in what sequence.

And don't try to memorize it, because you got junk in your head doesn't help.

Next item is PV.

We know we don't know the PV.

We could do the PV, but we don't know it.

What is the future value and where is it sitting?

It's not sitting in cell A1, it's sitting in cell A2.

Remember, what's sitting in cell A1 is the future at year 60 and

you want it at year 50.

So let me see what I did.

You can see, I can guess when I'm doing something not quite right.

So you have A2, 240.

You see, I told you you should put zero there and somehow I put a zero and

it disappeared, but I have intuition.

And once you start doing this number, a number will jump out at you and

say that doesn't make sense.

[LAUGH] So saving $3,000 a month,

just doesn't make sense today to get $8,000 in the future.

Look how much are you saving.

You're saving about $732.

15:06

Basically, what we have done is we have solved the problem where

we started out wanting 8,000 a month, 240 times.

We figured out its present value at this state.

You figured out, it's present value at this stage.

And then we said, how much do you need to save every month to solve this problem?

Look I'm not going to enter the items here, we already did this.

What I'm going to enter is what did we get over here?

We got 732 and I want you to think a little bit about it.

Look at the power of time in compounding.

I have to save only $700 a month plus 730.

But in return for that, I'm able to enjoy $8,000 a month.

The thing that has changed this time between the two.

Why is it that I can save so little and enjoy so much in the future?

One, because time has passed.

Two, because of the interest rate.

I repeat again, an interest rate of 8% a year,

which is 8% divided by 12 a month is a very high number.

First point.

Second point, yes, you are working hard hopefully,

to get the saving possible of 700 plus.

But remember, who's giving you the benefit?

The world is investing your money in good ideas, hopefully.

And we'll see what good ideas, later today.

That's the topic of today's class.

You are able to enjoy what the world has to offer through the ability

to invest in other things, so that other thing we call was portfolio.

But remember that portfolio grows over time, simply because of two things.

Movements mold the growth.

Higher the interest rate, higher the growth.

The two together is the profound effect of compounding,

which Albert Einstein said, he couldn't fathom.

And turns out that's why you need Excel and

other things to calculate these numbers.

So, I hope this put everything together one more time and

the small twist of going from a year to a month helped.

Do one last thing.

Answer the following question.

17:35

If compounding is monthly and the stated interest rate is 8% annually,

what really is the annual interest rate?

I can give you the direction of the answer.

It has to be more because of pause, compounding and

I would take your time to solve that problem and we are not going to do it.

You have a formula, you have information.

Do it for yourself and it will help you understand.

The only difference is if going from months to a year instead of a year,

it took many years.

Again, just messing around with the time line.