Alan Cring Productions in association with the Emergent Light Studio presents
the Illinois State Collegiate Compendium, Academic Lectures in Business and Economics.
This is Business Finance, FIL 240 for spring semester 2024.
Today, present value and future value.
And then after 20 minutes before the end of class, you have a quiz to take.
So we will begin without further ado.
First a quick look at the numbers, just have a look to see what's going on out there in the market today.
And as you can see, this is a bull day, but it's not a spectacular bull day.
It's just kind of trying to decide if it wants to be happy.
And as you can see, the Dow is barely up. It's just kind of wobbling around, break the water level.
Oh no, you don't get to see it.
Thank you.
How long did I do this?
Okay, as you can see, the Dow is just kind of wobbling around surface level.
But the S&P, the Dow is up 0.15%.
The S&P is up more, as one would probably expect, given that it's a riskier portfolio.
It's up 0.59%, and then the NASDAQ is up a decent amount, 0.86 so far today.
So we've got some momentum up. It's just not a roaring up kind of day.
If you come over here and you check over to see what the bonds are doing, the bonds are actually,
yields are down, which means prices are up, which means investors are buying bonds.
And they're also buying stocks, which means that there is a general level of confidence
in investing in any kind of security right now.
Confirming that more, as you can see, gold is down.
It's about to make it back below that break line at $2,000 an ounce.
That's more good news. Gold is bought, and price goes up, when investors are very, very concerned.
And right now we see that they are not concerned.
They're using their money and capital to buy stocks and to buy bonds.
So those are both good news. Even better good news is that crude oil,
it was, the trading range it's been favoring for a couple of years now has been 72 to 79.
And it was up there kind of close to 79.
Matter of fact, I think it punched through for a little while, last week was it,
but it's well down back towards the center of that trading range now.
It's 76.54. So we got to, there's not anything to worry about,
about gas prices going through the roof.
All of those are indicators of a good economy, and we should hope that it will stay that way.
On the other side of the world, however, the Nikkei, right at the bell last night,
which was their morning, it was down.
And then it just sort of piddled around, and there was a bull rally there towards the early afternoon,
but by the end there was a surge of bears one more time, one last time, so, alright, there you go.
But London, it had a good surge through the morning, mid-morning, and then it just sort of topped out,
there was a little sell-off, and then it just bobbled around.
So that was not the case when the sun rose, set over there, and it rose over here.
We were in a pretty decent mood.
We had a bull upswing at the beginning, but then the bears took over, but they couldn't quite kill it.
So after that bear run in the earlier morning, it began to come back up, but it was, like I said,
it's not a spectacular bull day, but we'll take our bull days wherever we can find them.
And that's the way it is.
Now, let me come over here, just a quick little lesson in investing.
I'm going to look at a stock called Nvidia.
You may recognize that I've shown it before.
It's a very risky stock.
Now, Nvidia, in a week, is going to report its last quarter of 2023 earnings.
Every company gives an estimate of what it thinks those earnings are going to be when it reports,
but then the markets have to assess, well, are they going to be, are they right,
or are they too optimistic, or are they pessimistic?
So in the days before the earnings are released, which will be on the 21st of February,
we should see maybe some kind of activity.
And if we look here, we see that Nvidia actually is up.
So there is an expectation.
Let me take you down here to show you the earnings.
As you can see, Nvidia has beaten its earnings.
The past four quarters, in the last two quarters, it estimated,
and it came in well above the estimate.
So the expectation is that they will come in above their estimate again this time.
What actually happens when they say, our earnings, they're saying they're projecting $4.50 a share.
Investors are kind of thinking that it might be more like $4.75 a share.
There's an old rule, and I think I've mentioned this before, but maybe I haven't,
buy on the rumor, sell on the news.
In other words, in the run-up to that earnings date, the earnings call,
then we should see optimism, they're going to be above, or pessimism, they're going to be below.
As you can see here, there's optimism.
Generally speaking, there's optimism.
They're going to have a good earnings report, probably maybe better than what they said that they earned.
Now, this is two-part, buy on the rumor.
In other words, the rumor is going to be that they're doing good.
They're going to report very good.
However, the other part of it is, you sell on the news.
Why would you do that?
Because the rumors, okay, let's say that the rumors were right,
and Nvidia is going to report earnings that are above $4.50.
Well, that has already been impounded in the price.
That's what the run-up has been all about.
You're not going to get any more out of it by holding it any longer.
Now, if they come in and they say, well, our earnings sucked, we didn't know it, but they sucked,
well, all that run-up is going to just evaporate, and the stock is going to drop.
So in any case, the rumor, and if they come in right on the earnings, well, that's already in the price.
Matter of fact, it'll probably drop a little bit if they thought it was going to be better than that.
So there's no reason, no game to hold on through the earnings call.
You buy on the rumors either way or sell if you think they're going to go down.
But when the news comes out, you should be out of the stock by then.
That way, because you're not going to get anything out of it,
and it could be that you're going to get your ass kicked because the rumors were wrong.
So get out, so buy on the rumors, sell on the news.
It's not just a folk saying.
It actually has a logic behind it.
Just thought I'd share that with you, and if you notice here, NVIDIA is a risky stock.
It is at 1.68 on the beta.
It is also substantially overvalued at 96.39 on the PE ratio.
So even though good news may be in the offing for this earnings report,
I mean, inevitably it's going to go down somewhere along the line.
It's going to drop away.
So that's where that all hangs.
Now I'm going to do something here.
We're going to move on to the fun part of the day.
And I'm going to do a couple of things here.
First things first, if you'll bear with me,
I'm going to show you some stuff in Canvas for your benefit.
Go into the student view here.
Student view.
Yeah, there we go.
So you'll see up here what you see.
A couple of things here.
First thing to show you, and I've mentioned this before, but I want to emphasize it now,
go to your files.
Now in files, drop it down, spreadsheets.
Now in these spreadsheets, and I'll tell you which ones are specific.
The names are pretty indicative.
But these spreadsheets are for the purpose of providing you templates to do problems,
almost any of the problems that you would encounter in this part of the course and on,
where we get more mathematical.
And I've gone through this little history before, and I just want to emphasize this again.
For ages, the way you did finance problems was with paper and pencil,
and maybe you had those ginormous tables that you were using in your accounting classes.
For over a century, that's how we did it.
And then in 1975, there was, well, okay, calculators started getting more common in the early 1970s,
and there was a big brouhaha in academia.
Well, we shouldn't let them use calculators.
They should use paper and pencil and times and divide,
and maybe they can use a slide rule, which was a mechanical device for doing multiplications and divisions.
But the first scientific calculators that were available to the common people
were brought online by Texas Instruments.
CASIO was in there too.
The Texas Instruments SR-70 and SR-71.
Well, God forbid we should allow students to use calculators in a classroom.
That's just an abomination. Never.
So being the kind of asshole I am, I started having students use calculators,
but I didn't do it right away because not every student could afford a calculator.
Once I knew that calculators were cheap enough so that anyone could get a decent one, we went to calculators.
Well, that still left those tables in place.
But then in the early 80s, two things started to come about.
One was that financial calculators started showing up.
The Triumph was in the early 80s, which is still sold to this day.
I still have one of them. It was an HP12C.
It was unbelievable how much it could do with what I show you.
There was one big problem with it. It didn't use algebraic notation.
It used an alternative called reverse polish notation, RPN.
So in other words, when you did calculations, you didn't say five times four equals.
You did five enter four times.
There was no equal sign on the calculator.
Okay, well, Texas Instruments came along and changed all that with its TI-80 series.
The 80, the 82, the 83, plus Silver Edition 84, and then a Monster 89.
That was a game changer.
However, another thing was starting to show up, too.
Spreadsheets. The first one was called Supercalc.
And then it along came a giant leap called Lotus 123.
And it was a standard even into the 1990s.
Another one that started to pick up speed was Quattro or Quattro Pro.
But then Microsoft came along with all of its shenanigans and violating antitrust laws.
And everyone turned to Microsoft, even though what it was doing was patently illegal
in the way it forced the other creative software out of the market.
One way or the other, Excel was the standard.
God forbid we should allow financial calculators or spreadsheets.
And that's as far as right now is concerned, most professors have a fit
if they hear that I'm using financial calculators, and they just have a cow
if they know that I tell you.
If you don't understand how these spreadsheets work,
you can get about any quantitative problem done that way.
Yeah, it's weakening one's skill, how to look up in a table,
but then again it's strengthening your ability to function in the workplace in the 21st century.
So that's where we are now with these spreadsheets.
And I'll be bringing them up, we'll build them again from scratch
so that you understand how things work.
Let me pull one up right now real quick, and you don't have to know this,
but I do want to point out how these little animals work.
Oh, and there I did it again.
Okay, you download over here on the three vertical dots, download.
And now let me pull it up.
Now all I'm doing this for is so that you can see how I construct these.
These are internal rates of return, profitability index, net present values, and all that.
And in some of them I've even put a graph in there that will help you along.
But let me pull up another one here, NPV and IRR.
This is a good one.
Let me pull this one up.
This gives you the feel of how I set these up.
And this is also giving you a way to think about how you want to do modeling.
What happened there?
That's not what I wanted.
Let's try this again.
Did I download it and then miss it?
Downloads, NPV, IRR, present value.
There we go.
This is a good example.
Now the way I construct them is that you have a color key.
Do not put anything in the orange box or the slight peach box.
What comes out, what's calculated by the spreadsheet, is in the pale blue box.
Everything else is what you would put in.
You just take the word problem, pull the numbers out, and punch them in there.
I've been teaching math this way since the early 1980s at Ohio State when I taught math.
Get the numbers out of the word problem and then throw away the words and then just get the problem done.
That's what you're doing here in Excel.
This is one of the templates that you'll be able to answer questions that will make you look like a hero of finance.
We do it with Excel now.
That's just how it's going to be in this class.
There's no tables and all that kind of stuff.
There's where that stands for it.
Let me take here.
In these spreadsheets, there's one for every class, every different type of quantitative problem that you could encounter.
Now, there's some tails and odds and ends.
You'll see that it's probably smarter, better, for you to just use a calculator instead of Excel.
In some of these problems, it's sort of like taking arithmetic and applying a quantum computer to it,
especially these first couple of problems I'll show you today.
Just use a calculator for those.
Now, as far as calculators go, I'm going to show you something else here.
A little bit of history again to bore you.
Where is files?
Okay, I don't want to go back up to files.
Now, I told you about financial calculators and scientific calculators coming out.
Back a long time ago in the 1980s, Texas Instruments provided a limited number of virtual versions of their calculators
to professors and geeks so that they could see if these actually were good and they'd like to use them.
Well, Texas Instruments provided, I got one of these.
It was a zip file and you open it up.
Then that was around for about 10 years.
I would say, if you're a student and you don't want to buy a calculator, here's the virtual version of it.
Then it disappeared from TI's website.
They kind of hidden it so normal people couldn't find it.
Somehow it popped up a few years later in Google's websites.
Google had taken over.
Then very quickly they locked it down so no one could get it and no one has seen it since.
Except that I had all my old floppy disks and I had it.
You can too.
Now, if you download this and then you share this with every ho handle on social media,
I will find you and I will tell the world that you hate Taylor Swift.
God help you after that.
Let me show you how you do it.
Now, this works only for a PC.
The heavy duty math, anything math, is not going to be on a Mac.
That's why we recommend when you come to a college like this is you get a PC instead of a Mac.
You're on your own if you've got a Mac.
But if you've got a PC, a laptop, desktop, down here at the bottom, see virtual TI-83 calculator.
Well, let's download that.
Okay, so now I'm going to go over here to downloads.
Now follow with me.
When I show you how to do this, follow with me.
It's a few steps to extract it and get it where you want it.
Downloads.
Well, there it is right there.
Now what you're going to do is you're going to right click on that.
That's a zip file.
You're going to right click on it and you're going to go down.
Okay, seven zip and extract the files.
And it'll say, okay, here's extracted.
And when you extract it, what will happen is you'll get a folder.
Now a folder, you have to go through a couple of layers.
Now one thing that I recommend, don't leave that folder in downloads.
If you're like me, every now and then you delete all those accumulation of downloads.
You don't want to delete this.
I usually just scoot it over here to my documents.
Okay?
Just somewhere where it will be safe.
Now let's go in there and look in documents and we'll find that folder.
I said we'll find that folder.
Where did I put it?
Son of a...
There it is.
Okay, there's the folder.
I did it for the last class so you're seeing it twice here.
Double click on it.
Is there some reason this sucks?
Oh, there.
And we'll come to folder VTI 83.
Double click on that one and you'll see a blue icon.
That's an executable file.
Now you can leave it there and every time you want the calculator you can go rummaging around to find this.
I recommend that you right click and go down, show more options, and you send it to the desktop.
That way when you want the calculator you can just click on the icon on your desktop.
Let me show you.
There it is.
And whenever you want the calculator it will be on your desktop.
Now watch this.
That's a real TI, except it's not real.
It does everything that the actual TI calculator does.
Amazing stuff.
It looks, it has all the functionality.
In fact, the stupid thing even turns off after a minute to save battery,
which just irritates me to know, Ed, that it does that.
But look at this.
In the TI 83 Plus, and this is very popular among finance people,
it has a set of apps called the finance apps.
Apps, finance.
And almost anything that I would have you do in this class is here in these apps.
It's just amazing.
It can do anything you want.
And you'll see me.
Sometimes quite, just realistically, it's faster to do it on this calculator than it is in Excel.
The problem with doing it on a calculator and instead of Excel is that you don't have a document.
You don't have a record.
You don't have a printable sheet or a file that you can send to email to someone else.
It's all there personally for you.
So that's the downside of using the calculator.
But, like for example, enter.
Suppose that I wanted to get a loan for five years, and I'm sneaking in some things here.
Five years and 12 payments a year, so that'd be a total of 60 payments.
Let's say the APR on the loan was 7.99%.
Now this is weird.
Financial calculators are the only place you do this, but you don't put the decimal in.
You just put in the percent as a number.
In Excel, in the outer part of this calculator, it would be.0799.
But if you're using a financial app, a finance app, a BA2, a TI-83, anything like that,
you will put in just the percent.
Just remember that.
And I have to divide that by 12 because it will recalculate every time you make a payment.
Now, we're going to buy a car.
It won't be a fancy car.
Let's say you want a car.
You want to borrow $25,000.
One thing about calculators is that present values are always entered as a negative,
and your answer always comes out as a negative.
That is just something that's been there since the dawn of these financial calculators.
Just don't forget that you put in a negative.
So in this case, I'll put in negative and use the negative sign.
Don't use the minus sign.
Use the negative sign.
$25,000.
Now I go down.
We're going to calculate the payment, so leave that alone.
Future value would be if you made a kicker payment at the very end.
Leases are like that where you pay an extra amount and you get the car.
Leave the rest of those alone.
Whatever you have been told in any other class, leave them alone.
Now down here at the bottom, it's end because you'll pay your payments at the end of every cycle.
So I'm going to take it back up here to PMT.
Alpha, solve.
There it is, $506.79 a month is what you'll pay.
That fast.
And actually, doing it on this calculator is kind of faster than it is in Excel.
I mean, I can just go through and do what ifs.
What if I decided that I wanted to do six years instead of five years?
Six times 12, we'll go back down and just recalculate PMT, put it on the PMT, alpha, solve.
Okay, $436 a month.
So as you can see, these calculators have a lot to say for them.
And you have one now for those times when the first formulas I give you,
they are so simple that it would be kind of ridiculous to use Excel to do them.
It's easier just to use the calculator.
Now in order to get out of apps in this calculator, you say second, quit.
You're back on the front screen.
You are fully able to use calculators and Excel on quizzes and exams in my class.
And that's because I'd like to have you ready.
I don't want to get you ready for the great jobs of the 20th century.
You've got to be ready for the great jobs of the 21st century.
And this is moving in front of us at an incredible rate.
Within a year, I probably have to teach you how to use chat GPTs to do these problems
instead of calculators.
As a matter of fact, my advanced finance class, I'm having them build chat GPTs right now
so they can do the problems that I'm having you use Excel to do.
It's that fast. It's happening.
So there you are.
That's where we are right now in the state of, and it's not just finance.
This is everywhere in business.
And businesses are, some of them are right on the curve.
Some of them are behind the curve trying to catch up.
Some of them think they know what they're doing and they don't know jack about what they're doing.
It's ridiculous the mess that it is.
Getting you guys in there with a clean set of skills, well, you'll be the heroes.
You don't get overrun by the imbeciles.
Okay.
Let's see why I'm bothered.
Oh well.
Madam, you have come to me and asked me if I will lend you $20 for a year.
Now I've calculated in my mind level, timing, and risk.
Well, the level, I can handle 20.
Timing, you know, I can hold off a year.
And the risk, okay, we'll go with it.
Okay?
So I'm about to give you this $20 and you say, I'll give you back this 20 in a year.
Catch you in a year, brah.
Okay?
This is a one.
I tried that at the Walmart and the security came and beat the crap out of me.
No.
20.
Okay.
You're going to give me $20 back in a year.
You said, I'll give you $20 back in a year and I say, you can kiss my old wrinkled ass.
No.
Why not?
What happened to the deal?
Anything?
Well, of course you don't.
But then I'm going to tell my cats to go and find you.
And I will feed them for a day.
It won't be pretty.
This is a bigger problem.
Okay.
Sir, I lend you $20 for a year and you give me back $20.
What's the problem with that?
What's the problem?
Well, yes it is.
But there's a reason why it's less now.
Now this doesn't have anything to do with inflation and all that kind of stuff.
It has to do with a fundamental thing that is recognized fully and it drives a capitalist system.
And it is this.
See, if I give you that $20 and you give me the $20 back in a year, I gave up the use of the $20 for a year.
Regardless of inflation or other factors that might impact the purchasing power, the very fact that I gave up $20 for a year.
I could have used this to get a grand slam breakfast at Denny's with the Happy Meal Kicker of the toy and the apple pie and the big cup of black coffee that nearly made me vomit.
I gave all that up for you.
So I just...
Okay, yes, we've gone through a lot together.
There was Berlin, 1987.
You saved me from those Sazi spies that had caught me off guard.
It was an ugly situation.
There was a gunfight, but I managed to get out of it.
We got that defector across the border and he told the CIA about the things that the Russians had captured from that alien spaceship.
That's gone now, man.
We've got to work in the present.
$20.
You see, at the bottom line, that's what we call interest.
The interest rate aside...
And I'll show you, interest rates have a lot of things in them, different risk factors and all that.
But at the very core, all interest rates carry an opportunity cost of foregone consumption.
An opportunity cost of foregone consumption.
That is at the core of every interest rate.
I've given up something so I get a reward for giving up what I could have done.
That Denny's breakfast.
And there would have been enough left over for one of those 30 cases of White Castle cheeseburgers at White Castle in Joliet.
You ever been there?
I know the people working there.
I went in one night and the big old woman said, what do you want?
I said, what I want ain't on the menu.
She said, shut up and give me your order.
Yes, evil mistress.
You know it's really hard to do comedy about present and future values, but I try.
God knows.
Look, the thing is that there's another part to this.
You see, you sir, I hire you to work for me at $4 an hour.
I'm not buying you.
I'm renting you.
Rent a guy.
That's all it is.
There is no purchase.
And that's the same thing with money.
You don't pay a price for money.
An interest rate isn't a price.
It's a rental rate.
Just like that wage, I am renting you by the hour.
And just like when you rent an apartment, you're not paying a price.
You're paying a rental rate.
So interest rates are not, sometimes you'll even hear me stumble and say, well interest is the price of money.
No, it's not.
Interest rates are the rental rate of money.
There are different rental rates for different kinds of funds.
There's a rental rate for short-term money.
There's another rental rate for long-term capital.
But they all are rent.
You're renting some kind of money or capital for a certain period of time.
When they lend you money at the bank or capital at the bank for a car or for a home,
you are renting money from them.
The rental rate is the APR, as they call it, the annual percentage rate.
But it's just a rent.
Okay, now, let's do a couple more.
You, madam, came into a nice pile of $15,000.
And at first you think Macy's is open online 24 hours a day.
That's what I would do.
Walmart, and I've told you, I'm a Walmart ho.
I go there all the time.
But you decide, okay, fine.
I'm going to put that money away.
So I'm going to start with this.
You deposit $15,000 into an account that pays 5.75 percent
compounded quarterly.
What will you have after 15 years?
In other words, I'm looking for a future value.
Know the present value, $15,000, but I'm looking for a future value.
Now, this is where we bring up the core formula.
All of the more complex formulas that you'll see, the book insists on showing you,
I'm not even going to beat them over the head too much.
But the core formula that is the spawn of all the others is pretty simple.
The future value, FV, is going to be the present value, PV, times one plus the
interest rate to the T power.
However, we have to stop here.
The R and the T are a little bit more complex than what you might think.
The R is the periodic interest rate.
And the T is the number of periods.
In other words, that APR that I gave you, 5.75 percent, that's not what R is.
Watch.
Okay.
Let's say the APR is 8 percent.
Number of compoundings per year.
Then the periodic interest rate R in the next column.
And then one column over the number of compoundings per year.
Now, suppose that we say annual.
That would mean one compounding every year.
R would then be 8 percent divided by one, which is 8 percent.
I can do basic arithmetic.
It's just when you get a little bit more complicated, I start making mistakes.
And T would be, in this case, let's say it's 15 years.
T would be 15 times one.
In other words, there would be 15 years, but there would also be 15 periods.
Because there's only one period in each year.
Suppose that we go to semi-annual.
That would be two compoundings per year.
So the R would be 8 percent, the APR, over two, which is 4 percent.
And so the T would be 15 times two.
In other words, there would be 30 compoundings in a year over the life of the instrument.
The next popular one is four, quarterly.
And in that case, the R would be 8 percent divided by four, which would be 2 percent.
And T would be 15 years times four quarters.
So in other words, there is a total of 60 quarters.
The next one would be monthly, which would be 12.
So this R would be 8 percent divided by 12, which would be 0.67 percent.
And the number of compoundings would be 15, T equals 15 times 12, 160, I think.
Now, the next one is weekly.
Now I'm going to try this real quick. Madam, how many weeks are in a year?
Thank you.
Say that again with confidence.
52? Yes, I mean you get all over the place. It kind of bothers me anymore that I get a lot of questions about how many weeks are in a year.
It's 52, darn it.
So in that one, you would have 52, and that would be 8 percent divided by 52.
And if you think I'm going to try to do that in my head, you're wrong.
And the number of compoundings would be 15 years times 52 weeks per year, and whatever that would be.
That's how many weeks would be in 15 years.
But then you have one last one that is of interest to us, daily.
Okay, let's try this.
There's two answers to that.
365 or 360.
Now technically you use both.
You would use 365 for 8 percent divided by, but you would use 365 for 15 years times.
I think the homework, they have you just do the 365 both.
But in real calculations, you would do it with the 360 and the 365 together.
Now where did that 360 come from?
The official explanation is that there are 360 traditional bankers days in a year.
There were five holidays for many, many decades.
But the actual reason, and I could show you but I won't, back before calculators and all that,
there was an arithmetic trick for dividing by 360.
And I was taught, I don't even remember where I was taught, but it's weird and it works.
But that was why they really used 360 as a divisor.
It's because you could just do this little trick, move the numbers around a little bit and all that.
But what were they are?
Okay, now there's actually one even faster.
There is instantaneous.
And you'll never see it.
It's provided for accounts only of the very wealthiest people in the world.
But instantaneous compounding doesn't even use that normal formula right there.
It uses the natural constant E to the power of the negative R or something like that.
So don't worry about that one.
Just ignore it.
But those are the traditional ones.
Now one quick side comment.
There are two prefixes that are, just to keep them in your mind, I won't do them on a quiz or an exam,
but the prefix by, B-I, that means every other.
So if I said bi-weekly, that would be 26.
Bi-monthly would be 6.
Now the other one, semi.
You see it right there.
Semi means twice every.
So semi-annual would be two times a year.
Semi-weekly would be two times a week.
Those two are out there.
You might run into them.
The one you do see is, rather commonly, is bi-weekly.
Because a lot of companies, if you're a wage employee, they pay you bi-weekly.
Or semi-monthly.
As a matter of fact, if I understand it right, some of our salaried staff here is paid semi-monthly
to get a check on the 15th and a check on the last day of the month.
So they are out there.
So just to keep it in your memory that those two show up.
But I'll stick to these for anything that I would give you.
But now we come to another side.
Another problem.
Madam, do you know that I am going to die someday?
It won't be while this class is running.
I guarantee you.
I will come back from the grave to finish it.
But it turns out that you're my daughter.
And you just found out that I'm going to bequeath you $250,000.
Yay!
So now you're just checking the web to see if there are any places that charge a modest fee to off an old geezer.
But as it turns out, actuarially speaking, you hear the life expectancy of a North American male is 77 years.
Actually, that's not how you think about it.
You use conditional probabilities.
For example, if you reach 65, then the high probability that you'll live to 83.
That's the life expectancy if you have made it so far.
In other words, conditional probabilities.
So you're going to figure out, okay, that old geezer, he's probably about 65 and he lives to 83, so that will be 18 years.
So you're going to get $250,000 in 18 years.
What would that be worth if you tried to get the same amount now that it was worth in 18 years?
Okay, so you will receive $250,000 in 18 years.
If the discount rate is, let's say, 8.9% compounded, let's say, semi-annually,
how much is that worth now?
In other words, here, you want a present value.
Well, the core formula, all you have to do is turn it around.
So that I divide both sides by 1 plus r to the t.
So the future value divided by 1 plus r to the t is the present value.
So those two are the core of all finance formulas that you would probably encounter.
Now, a little side comment here.
You'll see me oftentimes do this.
Instead of fv over 1 plus r to the t, I'll do fv times 1 plus r to the negative t.
You remember from algebra, it's long ago, the reciprocal is the negative of the exponent.
Now, the reason I do it is this.
It's purely practical.
When you divide, if you've got a complex calculation in the denominator,
you're asking to forget a parenthesis or something and get the wrong answer.
This way, it stays all on one line, and all you have to do is remember to put a negative on the exponent.
That's the only reason.
You can do it the way that second line, but the third line, is just less likely to get you into trouble with it.
So now we've got our two formulas.
Over here, we'll use the future value.
The future value will be $15,000 times 1 plus r.0575 over quarterly 4 to the number of years 15 times 4.
Don't forget to put that exponent in parentheses for God's sake.
Yes?
What did you get for.0575?
.0575, I forgot the 5.
Thank you.
The percentage.
Sorry about that.
.0575.
Now remember, you're going to do this on a calculator.
Just straight up run the calculator, which I'll do.
You would use.0575.
But if you're using a finance function of some kind, you would use 5.75.
So if you use a calculator or Excel, it's.0575.
Now over here, we've got a present value.
So the present value on this problem would be the future value, 250,000 times 1 plus,
the APR here is.089 over, where the hell, semi-annual 2, to the negative 18 times 2.
And again, don't forget to use parentheses on that exponent.
So now we'll just lock and load those and get it done.
It turned off.
Why does a calculator save battery that doesn't need a battery?
Okay, anyway.
I'll do the future value first, which is, if I can see that far over,
15,000 times, open parenthesis, 1 plus.0575,.0575 divided by,
what was the compoundings on that?
Quarterly.
Quarterly, thank you, divided by 4, close the parenthesis.
Now we raise that to the, and open parenthesis, you want to trap that,
what was that, 15 times 4, close the parenthesis, and there you go.
$35,318.60.
Now I, almost always, it's a little different in a few cases,
but usually I'll just say, to the nearest dollar,
and I'll give you a couple of dollars each way, so you would put in an answer,
35,319, but I'd give you the credit if you did that dollar off either way.
Now the other one, 250,000, this is the present value, times, open parenthesis,
1 plus.089, close the parenthesis, to the, now open parenthesis,
and now here, don't put in a minus sign, put in the negative, right there,
that negative, 18 times 2, close the parenthesis, about 116,000, no, 11, my ass.
Oh, I see what I did. Want to see a trick?
I don't have to key in the whole thing, I can say, use the yellow button, enter,
and look at that, it comes back up.
I forgot to put in the, divided by 4.
So I've got to do insert, second insert, divided by 4.
Yep, enter, 113,000, that's better, 113,210 dollars.
Now, how do you get rid of this calculator?
Right click, exit without saving state, and it's gone.
Okay, now you've got a quiz, and once you do your quiz, that's all I have for you today, I thank you.