Alan Cring Productions in association with Emergent Light Studio presents
the Illinois State Collegiate Compendium, academic lectures in business and economics.
This is Business Finance, FIL 190 for spring semester 2024.
Today, present values and future values.
You will have a quiz, a ten minute quiz, and I will let you start on that at 10.35 this morning.
But other than that, we are just going to have a happy time here today.
First of all, looking at this.
We have a bear market and a bull market.
This one is a kangaroo market, down massively and then up substantially today.
It's not a spectacular day yet, but it's a strong sustained upward momentum in the market right now.
So without further ado here.
As you can see, it is a bull day, definitely a bull day.
You've got everything green.
And so there is a decisive trend.
And if you'll notice, see these spark charts?
Well this one, the Dow, I don't know what happened there.
But there's a generally consistent pull upward.
There may be some corrections along the way, profit taking and all that.
But at the same time, it seems to be showing signs of life.
Yesterday was one of those days that was just pure suckitude across the board.
And dragged down one of my high beta investments into the earth.
And now it's pretending like it doesn't notice that the market is going up.
So that just irritates the hell out of me.
But anyway, let's go back over here and have a look.
Now as is typical, the Dow is up the least, the lowest risk portfolio.
And then you've got the next at.22%.
And then the S&P 500, this early in the morning it's up.60%.
And we've got the NASDAQ up.81%.
The classic risk return.
The classic risk return relationship that you usually see, we see here today.
Where we want to go over very quickly and have a look at the bond market.
And as you can see, that there the yields are falling.
Which means the prices are rising.
Which means investors are pouring money into the bonds as well.
So we've got a broad based rally of both equities and debts.
Bonds, both of them heading on the upside, heading upward right now.
So that would show a lot of confidence.
And matter of fact, all those three basis points down on the bond yield.
Coming over here, where the heck am I?
Oh, just a quick note here.
Notice gold is down.
So in other words, the highly defensive commodity is pulling back.
So investors are saying, let's get into the risk and out of the safe harbor.
That's all good news.
In other words, you're getting multiple signals of a strong bear market.
Even if it's not up spectacularly yet, this is a good sign for you out there who are bulls.
Now again, I emphasize for investment people, for finance people, everyone thinks,
well we make money in bull markets, we lose money in bear markets.
That's not true.
You can make as much money in a bear market with equities dropping.
As you can in a bull market.
I'll show you how.
It's that side of the market where people don't think there's a way to make money on the downside.
Well there are plenty of ways.
Well short selling is one.
Put options is another.
There are plenty of ways that you can make money in a bear market.
We just kind of tend to like to see bull markets because that generally indicates
that the overall economy is doing well too in a bull market.
But that's certainly not the case that you can't make money in a bear market.
You have to be flexible in your thinking.
Crude oil, it's beginning to push a little bit scary toward that upper level of the 72 to 79 trading range
that it seems to have favored for several years now.
Right now it's up there bumping on the top end of it.
And a lot of that is just the general condition of the oil markets.
Everything from production levels at the well heads to how much is getting into the tankers and is on the high seas.
How easily they can get their tankers into the different ports that they would want to get into and all that.
And then how about the refineries?
Are they able to take that oil in and turn it into hydrocarbon products for different consumer groups?
It's all complicated.
It is a world of its own.
And it's actually, every time I've gotten into that world, I feel like I'm walking across the entire earth.
Because in one minute we're talking about reserves in the Middle East, in some country,
in another minute we're talking about whether or not VLCs can get into the ports that they use,
as opposed to the ports that are not big enough to handle the super tankers, all that kind of stuff.
So it's a fun world and it's not a world that I talk too much about in a class like this, unfortunately.
But moving on here, coming over here just for a quick look at the overseas markets.
The Nikkei was just in a pissy mood.
More or less it started out immediately down and then it just kind of floated going a little lower and then kind of rallying.
And then at the end, the rally, as you can see right there at the end of that spark chart,
this bull attempt to come back up above water was thwarted right there at the end by a little bit of a sell-off.
So there wasn't anything happy going on over in Tokyo,
so we'll let the sun set there and come over to our friends on the big island on the other side of the Atlantic.
And they had a pretty decent day there.
By the end though, you see that same profit-taking began to take hold there in London.
They're not finished yet for the day.
And that profit-taking just sort of came and then no more news came in and showed up.
So it's kind of floating right there toward the end.
On our side of the world, as you can see, we started up at the bell.
At the bell, we were already in positive territory.
And from there, it leveled for a little while.
As a matter of fact, the Dow dipped a little bit, but then a surge came again.
Some more good news, and I'm not sure what's going on this morning.
I haven't had a chance to talk to anyone or look at any of the back message boards,
but something is making everyone happy today.
Well, there's no news here.
Okay, a new stock price target for Nvidia ahead of earnings.
NVDA, risky AF, but we'll have a quick look at it to see.
Whoa, look at that, up 2%.
Now there's a stock that you might want to grab a couple of hundred shares of right now.
$736 in change per share on that.
So it's definitely not an average investor's pick up a round lot.
A round lot's a hundred again.
I don't think any of us could afford to grab a round lot of Nvidia.
But of course, you're taking that chance.
Look at that.
First of all, the beta is well above 1.
This is in highly risky territory.
This is for the serious risk takers.
And then the PE ratio, that's saying it's overvalued.
Well, whatever.
And of course, you've got an EPS strongly positive, $7.58 per share.
So there you go.
Everything looks good on the way into the earnings.
That dividend is about as lousy as you can get for a dividend,
which tends to indicate from looking at those very financial ratios
as you have that they're plowing a lot of money back into the company.
Very little bit of a dividend.
But if you look here at the earnings, their earnings are coming out in just a week.
And so this is rumor.
Buy on the rumor.
See how it's going up in advance of the earnings?
What we're seeing here is that Nvidia is going to say,
we will post $4.50 per share earnings.
But the market's already corrected, done that, because they posted that weeks ago,
what they think it is.
So what is going on right now is that the market's, the rumor is that they will come in above.
With the actual earnings for the quarter, they'll come in above $4.50.
That's what's exciting the markets right now.
So that's why it's pushing up, reflecting the rumor.
Now remember what I told you, it's not always true,
but the old saying is you buy on the rumor, sell on the news.
So if we get really close to the day of the earnings,
you'll see a sell-off of the old timers,
because we always know that it's going to spike.
If there's rumors that it's going to be better than what the company says they think it's going to be,
the rumors are going to push that price up.
And then when it comes in, whether it comes in above or below or at the earnings,
there's no more price momentum upward at that point in time.
Any momentum is going to be on the downside.
It's either going to do what the rumor said, and so there's not going to be a price spike.
It's going to come in at what the earnings were,
which is going to defeat the rumors and there will be a small sell-off,
or it's going to come in under the estimate and then there will be a serious sell-off.
So there's really not a whole lot of good news, good good,
in holding on through the earnings call in one week from today.
Just some of the old time advice and the learning you get from doing this
in the actual trading rooms and all that over the years.
Anyway, let me show you something here.
Get off this.
As I said, Excel is going to be our go-to for all kinds of happy things that we do in this class.
And as I said a long time ago, we would have done things with actual pencil and paper,
calculating formulas for present values, future values, and all that kind of stuff.
Then came the era of the financial calculators,
and there was a lot of resistance to those even to a few years ago.
There were some professors here who said, I don't allow financial calculators to be used.
If they want to use something, they'll use tables.
Tables were the thing from the 1960s onward,
and they're still used in a lot of academic courses,
especially those that are taught by older professors
or where those older professors are in charge of telling the new professors what to do.
So the tables are still out there.
You've got to use tables. You can't use calculators.
Well, come on. That's just ridiculous because those tables were generated from calculations done on computers or calculators.
Then came the era of Excel after the financial calculators.
It wasn't taught hardly at all except in a few elite colleges until the last few years.
Here, I use Excel to do the problems.
Now, don't get me wrong. Sometimes a good financial calculator like the TI-83 Plus or TI-84,
it can do things actually kind of more efficiently than Excel can.
The problem with using a calculator is you don't have a documented sheet
that you can print out or email to someone else or put up on a screen.
And that's the weakness. Even when the TI-83 or the TI-84 would be a faster way to do problems,
it's still, for our purposes, you folks are going to be in environments where you have to show this to someone.
That's why Excel, we do it.
And sometimes Excel is a little more cumbersome and you have to memorize a lot of things.
It doesn't take a lot, though. Don't get me wrong.
To do basic what I'm going to do in this chapter, you don't need to be a super hot Excel certified by Wall Street Prep
or something like that. You don't have to, for what I do in here.
You just got to know a few formulas and that's all there is to it.
And so we'll do that. But I do want to show you a couple of things here really quickly.
First things first. Let me go back up here to files and see if I actually had the sense
Here, this, okay, the background.
The slide rule calculators, as it were, started showing up in the mid-1970s.
And then from there, in the early 80s, some financial calculators, hardcore financial calculators started showing up.
HP, Hewlett-Packard had an HP12C, which was a beast at doing a lot of finance things.
And it was embraced, even though it didn't use algebraic logic, it used RPN, reverse Polish notation.
You got the hang of it because my God, that thing could do financial calculations like lightning.
TI came along with a couple of basic financial calculators.
The BA series, the BA and the BA2, and a few others.
And those can do a lot of financial calculations.
They're a little cumbersome to work with.
And I think the book even shows you, well, you can do this with a TI BA2, and they show you the steps.
And you can see that's kind of dodgy.
Then they came out with the TI8X series, 80, 82, 83, 83 plus and all that.
And they had a hidden secret. They had finance apps in them.
And I'm going to show you those in just a minute here so that you can see them.
And they passed this around as a downloadable in the 90s for geeks to see how it worked.
And it shows up as a TI83 plus on your computer.
And then it acts just like a physical TI83.
And they passed it around. It was a ginormous zip file containing an XE file and all that.
And that was, I mean, every geek who got a hold of one of these.
And then, interestingly enough, it disappeared.
TI stopped handing it out because obviously you get that, then you didn't need to buy a $150 calculator.
But there was still a TI site you could go to and find it, if you really were that kind of a person.
And then it vanished from there.
And then somehow it showed up as a Google restricted file.
Well, I had my old floppy disks and I had it.
And now you can have it too.
Now if you go out and blab to everyone and put this up on some full social media circus, I will find you.
But you can do this. Now understand this is not for Macs.
Macs are not financial computers. They just aren't.
And so this was never brought out as a Mac application.
So let me show you what here.
See this virtual TI83 graphing calculator?
You click on this and download.
Now follow with me. If you want this, it's yours.
Ow, I almost hurt something I care about doing there.
Now open the file.
Now as you can see, what's going to happen is this is a zip file.
The first thing you're going to want to do is...
Does this even have a zip?
Do they have a zip cancel? Let me do this. Let me try it this way.
This...
Open with.
It's a zip file. I know that.
Does this thing even have zip in it?
Okay, let's get back up here to the root directory.
Oh, it's not going to let me... This PC.
Windows.
Program files.
Windows, I don't... They got rid of... I can't unzip a file here.
Unreal.
Let me go up one.
See if it's in here somewhere.
Oh, 7-zip thing. Yes, yes.
Just once.
Well, does that work?
It keeps killing it. When I try to open it, it kills it.
Oh, hells bells and pigeon poop.
It's not letting me unzip it. You can do it on your own.
Just unzip it and you'll get an.exe file. You execute it.
And you go down a couple of directories and you'll see vit83.
Just copy that to your desktop, that executable vi file, and you'll have the virtual calculator.
I can't believe it's not going to... Let me try one more thing.
Real quick, I don't want to waste too much time on this.
But, let me go back up here to the PC and Windows.
Program files.
7-zip.
There we go.
7-zip.
I need the executable.
View. Details.
Is this an executable?
I can't tell.
7-zip.
Nope. They're not going to let me do it.
They're so afraid of anyone doing something. Open.
See, every time I try to open it, they've got some kind of a block on it.
So you put a program on the computer that no one can use.
And you can kiss my ass. I'll figure out how to do it and I'll show it to you next week if you can't do it yourself.
But trust me, it's really handy to have that calculator.
But anyway, let me go back here. Apologies for that nonsense.
Files.
Go down here to spreadsheets.
Now, in the spreadsheets, you're going to see some spreadsheets that are quite useful to you in this class.
You can calculate internal rates of return, present values, future values, internal rates of return, all of those.
And we'll build those, but the templates are already in there for you to be able to use to calculate present values, future values, payments, and all of that kind of stuff.
It's already there for you.
And let me look real quick here. Free cash flow, IRR, NPV, and IRR.
Loan payments, present values, there we go. No, quit that.
Present values and future values.
Download.
And this will allow you to calculate present values. It'll allow you to calculate future values.
Instead of using tables or formulas you calculate or a calculator, these will do the job for you.
The whole thing about doing these in Excel is just knowing the calling function.
What calling function is used to get a present value? What calling function is used to get a future value?
How about payments on a loan? These are all in the time value of money.
So we'll talk about this over the next few minutes and a little bit next week.
But you sir come to me and you say I should like to have $20. For how long? For a year. Okay.
So I say, well now in a year you say, well I'll give you your $20 back in a year.
And I say kiss my wrinkled old ass. Why am I going to say that to you?
Because you just, there's no reason, no incentive for you to do that.
Well sure there is. You're going to beat the crap out of me if I don't do it.
But the whole thing there is that you see there is a time value of money.
And at the heart of every interest rate out there is this underlying truth that I give you $20.
I don't have it for a certain period of time.
Underneath all of the other things like well inflation or risk or all that,
there's this reality that I have given up consumption from this for a year.
So at the heart of the entire concept of the time value of money is the opportunity cost of foregone consumption.
So when you look at financial statements, there's really not a, you can't just say, well last year, well,
sales last year were $21,000 and sales this year were $22,000.
Also, we've done better this year.
Well not really because I'm not comparing those numbers, they have dollar signs.
But you see that is a hidden convenience that hides something very important.
Very important because dollars or any currency or any value at all is time dependent.
We never put in dollars in 2023.
We don't put dollars in 2022.
We leave out that last part of the units.
The units are not dollars, the units are those dollars at the time that they occurred.
And so I can't just look at $22,000 and compare it to $21,000 because the units of measure are actually different.
The difference is hidden, we would never write it directly on there,
but for us in finance, we have to appreciate that that is what's going on.
Over time, if I were to telescope this back to here,
that $22,000 would look a lot more like $21,000.
Or if I were to take that $21,000 and bring it forward a year as a future value,
that $21,000 would look a lot more like that $22,000.
That's the time value of money.
Almost no one thinks in these terms, but it is the reality we have to appreciate.
Dollars are time dependent.
And so we have to use a conversion factor.
Like for example, one inch equals 2.54 centimeters.
We convert like that, that's a conversion factor.
Well, we have to have conversion factors in our business.
Now somewhere along the line, you learn unit conversions.
And they're static.
That is always the case.
One inch equals 2.54 centimeters, and a lot of other ones.
Three feet equals one yard.
They are what we call static conversion factors.
They are always the same.
In finance though, the problem is that they aren't always the same.
There is a variable factor.
Well, there are two variable factors.
There is the discount rate, and there is the time.
So the conversion factor would be different depending upon the discount rate and the time period.
That's what those tables that you used in accounting were.
They were the conversion factors based upon different interest rates and different times, whichever way they did.
So they were actually dimensional tables, but we in finance would like to kind of avoid using tables and look at the formulas themselves and use those formulas.
Either on paper or with a financial calculator or with Excel to get those dynamically as we need them.
And that in Excel especially is kind of nice because you can alter the parameters that drove the conversion factor.
Okay, instead of using a 2% interest rate, let's use a 5% interest rate.
And the conversion factor would instantly change and all of your results would change.
So, probably for the next, I don't know, 25, 35, 40 years, we'll show you a few of the formulas.
And I'm beginning to wean my classes off the formulas.
I show, there's kind of like a foundation, core formula.
And I would like to show you a few of the formulas.
And I'm beginning to wean my classes off the formulas. I show, there's kind of like a foundation, core formula.
And I will show you that and I will be showing you that until the Lord calls me home just to send me down to hell.
But, so I'll show you the core formula.
But past that one, I'm not going to really push it too much.
The future value, and this is for a lump sum of money.
The future, ow, God, the future value is the present value times 1 plus r to the t power.
That's sort of like the core driving formula.
This is for compounding.
I don't even go through simple interest.
And there's a problem with doing that because there are still a few places in finance that use simple interest calculations.
Specifically, in money markets, it's used all the time, the simple version.
I don't even show that anymore even though I probably should.
But let me do a couple of things here.
This is the future value.
Future value.
This is the present or current value.
Present value.
Now here is where the kicker comes in.
R is the periodic rate.
T is the number of periods.
Now this is important to keep in mind to remember.
Excel and a good financial calculator like the TI-83 Scientific, you still have to tell it how many periods per year.
So for example, the annual interest rate, the APR, let's say that's 8%.
And let's say that the, okay, let's say period the compoundings per year.
Now if it's annual compounding, then that would be one period.
So the R would be 8% divided by 1, which is 8%.
If it is semi-annual, that would be two compoundings per year.
So you would have the R in the formula would be 8% divided by 2 or 4%.
If it is quarterly, that would be 4 per year, so it would be 8% divided by 4 or 2%.
The next one that is important, and this one is very important in consumer loans and consumer debt, is the monthly.
And that one, it's 12, so it would be 8% divided by 12.
What is that, 0.67%?
I am really, really lame.
Give me a calculator, for God's sake.
Scientific.
Okay, 8 divided by 12.
Try that again.
8 divided by 12.
Is there some reason this sucks?
Oh, clear. Try it again.
8 divided by 12.
Now, the next one, if you had compoundings weekly, so what would weekly be?
54? 52.
I did that on purpose because I am appalled, mind you, appalled that folks these days don't remember how many weeks are in a year.
Okay, if it's weekly compounding, then that would be 52, so you would have 8% divided by 52.
And by the way, there is another one.
There are two other ones.
The prefix buy would mean that it happens every two weeks.
So bi-weekly would be 26.
Bi-monthly would be 6.
And then there is the other one, which you see there, semi.
Semi means twice every time.
So semi-weekly would be twice a week.
And then there are a couple of other ones from sesquicentennial.
I won't even try that one. It's like every one and a half.
I hope you'll never have to see a sesquicentennial.
Although a lot of towns have their sesquicentennial, which is 150 years the town has been around.
But I won't get into that.
Now, there is another one, daily.
Daily is an oddball.
Now some of your textbooks say just use 365.
However, in banking especially, you use 360 or you use 360 and 365.
And you're saying, huh?
But as a matter of fact, there is a teaching assistant in this class who went through that, seeing when we...
Okay, money market yields, money market rates are calculated on a 360.
But effective market rate, you then convert that to 365 days in a year.
Now where did the 360 come from?
Well, the traditional explanation is because there were traditionally five bankers days a year.
Five bankers days a year.
The actual reason, and I won't show you why, how.
But there is an arithmetic trick for the number 360 as a divisor.
And so it made it a lot easier in banking to calculate a daily interest rate.
Okay, but now the T would be the number of years times annual one, semi-annual two, quarterly four, weekly 52,
and for daily, if you use the 360 and 365 together, which is technically the way you're supposed to do it,
you divide the annual interest rate by 360 and you use 365 in the exponent there.
So, you put $1,000 into an account carrying an APR of 5.2%
compounded quarterly.
How much will be in the account after 15 years?
15 years.
So the formula is the future value is the present value times 1 plus R to the T power.
So in this case, it would be, well, we have right now $1,000 and the interest rate is 0.052 over quarterly to the four times a year for 15 years.
Now remember to trap things in parentheses for God's sake, because the order of operations, your calculator,
if you're using a calculator, you are going to, it's going to believe that you want order of operations strictly.
So what I'm going to do here, I'm going to drop this down and straight up, this one, it's ridiculous to use Excel to do it.
It takes longer to enter all the data than it would be to just go ahead and do it yourself.
So I'm going to take all this down, clear this out, and we're going to do 1,000 times, open parentheses, 1 plus 0.052 divided by 12.
Now notice I don't need to use a parenthesis for that division, because the division by order, the hierarchy of operations will come before the addition anyway.
But I do need now to close this off, and then I'm going to raise this, and this is where you have to put in parentheses,
because the only way that it's going to, it's going to take exponents first.
So if I just put in 4 times 15, it will do the exponent 4, and then times comes lower in the hierarchy, so then it would take the result times 15.
So you have to trap that in parentheses, did I do that yet? Nope.
So open parentheses, 4 times 15, close the parentheses, and now there's your Uncle Bob.
$1,296.20.
Now on a test or a quiz, I would not ask you to do anything more than round to the nearest dollar.
And I'll give you a little fudge of a couple of dollars both ways, in case you had a little finger fart on the keyboard or something like that.
So the answer would be $1,296.
And then I'd tell your test generator, take any number, answer between $1,293 and $1,299 as being correct.
Precision is very important.
However, there's something, now here's a little secret about time value of money problems, whatever they are.
If you make a mistake, almost guaranteed your number, your answer will look wrong.
It will be either a few pennies or a few tens of thousands of dollars for a problem like this.
If you forget to put the parentheses in that exponent, something like that.
Use common sense. Just go back and ask yourself, does this answer make sense?
On a quiz, one of my favorite stories, I gave a quiz to calculate a car payment.
The car was like a, back then, $20,000 car, six-year payments.
And several students got monthly payments that were around $10,000.
And one of them came up and complained, well, why is this wrong?
I said, well, look at the answer. Does a $10,000 payment every month on a car make sense?
And she said to me, I don't know, my dad bought my car.
So, that was what I thought about just moving to the mountains and save the hell with life.
But, it happens almost every semester.
So, just look at that. Well, he's holding, and that's not a great interest rate, put the money aside, about $1,300.
That kind of makes sense.
Now, if I got something that was $2.05 or $25,800, that would not have made sense to me.
That would not have been a reasonable answer.
A caution here. Most financial calculators, I would put in just 5.2.
Excel and arithmetic, you have to put it in as the decimal.
Or, in Excel, you'll see me do it, I would type in 5.2 and percent.
That way they visually look right, the way people use them.
But, percent, financial calculators, almost all of them, they let you put in percent almost everywhere.
You don't want to put it in the decimal.
You'll get the wrong answer if you put it in the decimal because they'll think that's the percentage.
But, anyway, there's that.
And, like I said, this is simple enough that, yeah, you could write a quickie little Excel routine to do it,
but it's just about as fast to do it with a scientific calculator.
Now, take this the other way.
Suppose that instead of running forward in time, we wanted to come back in time, get the conversion factor running backward.
We take that formula, FV equals PV times 1 plus R to the T power.
And I'm going to divide both sides by the 1 plus R to the T power.
So the future value over 1 plus R to the T power buys you a present value.
This is how we reel money back in time.
This is a very useful one.
The future value, yeah, it has a few uses, and one of them is very important.
But now, one thing you'll see me do, and this comes from your days in high school algebra,
you'll see me oftentimes write this as FV times 1 plus R to the negative T.
The reciprocal of the denominator is the negative of the power.
You'll see me do it like that, and I have a good reason, and it's just a practical reason.
When you're dividing, the more complicated the denominator is, the more likely you are to screw something up as far as the parenthesis goes.
If I put everything on the same line, it's just a little more likely that you won't make a mistake trying to,
where did I put the parentheses to hold this whole denominator together kind of thing.
It's just my habit, and I encourage you to get kind of into this habit too.
How you key in the exponent, and then you hit that plus-slice-negative button on your calculator if you're using a calculator to do this.
But anyway, there's that in it.
And so, in order to do this one, this lump sum,
what I would do here is, let's have a problem.
You sir, remember I told you you are my son? Yeah.
Okay, here's the problem. I am going to bequeath you $250,000.
Now, you very, you thank me, and then when I'm gone, you go check the actuary tables on mortality to see when I'm going to die.
And it turns out that you will inherit
$250,000 in 18 years.
Yes, that's what the actuarial tables actually would say my life expectancy is.
It's not as simple as, well, the average life expectancy of a North American male is 77.
It's not how you think about it.
You have to think in Bayesian terms.
The person who lives to 65, how many more years past that would that person live?
In other words, it's a conditional probability, but that's another thing.
So what we're going to do, if you discount cash flows at 7.4%,
how much is that inheritance worth to you now?
In other words, what we're saying, in a given interest rate environment, you would be indifferent between $250,000 in 18 years
and what we're going to find out for the number here now.
It's essentially the indifference point between the two amounts of money.
Because whatever I get now, if I got an amount now, I could put it in the bank at 7.4%
and it would become $250,000 in 18 years. That's what we're doing.
So in this case, the present value would be $250,000 times 1 plus.074.
Oh, I forgot to say compounded. I forgot. Compounded. Let's do it compounded monthly.
So we'll divide the.074 by 12 and then pop that to the 12 times 18 years.
The number of compoundings that will happen. 12 times 18 is the number of compoundings that will happen over the life of this problem.
And I forgot to put my negative sign here, talking while I'm trying to do stuff at the same time.
And if we crank this out, clearing this thing out, we would have $250,000 times, open parenthesis,
1 plus.074 divided by 12, close the parenthesis, to the, raise the power, open parenthesis,
12, I'll put the negative right here, positive, times 18, close the parenthesis, and don't forget to hit equals.
I say that because sometimes I forget to do that. It's worth $66,257.66.
66,258, rounded to the nearest dollar.
And again, you ask yourself, does this make sense?
Well, you know, if I'm going to have to wait 18 years for a quarter of a million dollars, yeah, I probably would be happy with about $66,000
if I could have it right now so I could go to Denny's and get the Grand Slim Happy Meal.
Indeed, a real finance for real people.
Now, you've got to open up, you've got a quiz to take, and then that's all I have for you today. I thank you.