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 at the appropriate time, I'll stop
the lecture, you have a quiz today. But before we begin that, all of that, a quick
look at the numbers. And I won't ask you whether this is a bull or a bear day
because it's kind of not one or the other. If you look there, the markets had
a strong opening for about the first hour and then it just kind of fizzled out
and the bears took over. The Dow was just bouncing around barely a positive by now.
It's just not one of those days where it could sustain the optimism that started
it up. A couple reasons for that, but going through and having a quick look at
the Dow is up about 0.12, that's nothing. S&P 500 is up a half a
percent and the Nasdaq is up three-quarters of a percent. So yeah, it is
sort of a bull day, but it just doesn't want to be a bull bull day. It's sort of a,
I don't know what you'd call it, it's not an enthusiastic run-up with no end in
sight to the upside of it. So, but the other side of it though is, some good
news there is that the 10-year bond, the yields are falling, that means prices are
rising, which means that there's demand for bond securities, but there's not any
sell-off of, real sell-off of stocks, so it's not a flight to quality kind of
thing. It's just that there is some enthusiasm in the bond market and the
yield continues its track downward. As I had said in the lecture on Monday, it's
trying to find its way down below 4% and every time it goes down, well that's
better news for the economy as that will lead interest rates in general down. Gold,
oddly enough, gold was trying to spike earlier, but then it's lost its
enthusiasm too, so it's not like investors are charging, running to gold
or anything like that. It's just not a very bright, strong bull market today, but
it isn't a bad market either. This is one of those kind of days of, meh, it's okay.
And as you can see, crude oil, it had been working its way up perilously toward
that upper end of that trading range of 72 to 79, and now it's putting some
distance on it, going back down. There were some jitters in the market, in the
oil market earlier in the week, it looks like they've finally calmed down, there's
not going to be any supply disruptions or anything like that. Good news there.
On the other side of the world, the Nikkei just couldn't find any reason to be
happy most of the day. It started out right at the bell in negative territory
and then it just kind of floated from there, a little bit down. You had a rally
there at the end, bulls were trying to bring it up above the waterline
there, but they didn't quite get there and there was a sell-off right at the end
of that. So Tokyo was not a happy place today, it wasn't anything terrible, but
just wasn't happy. Now interestingly, as of right now, and London is still trading,
but they had a little bit of a surge, well it was not that bad, but then after
some good news came through, it just sort of left it to drift and a little bit of
sourness there, but it'll probably end the day up, but not much more
than where it is now. It's just they had some good news and that was the end of
it. Let me show you a stock here. This one is, and I'm showing you this one because
its earnings are coming up I think in two weeks and so you've got activity
sort of like the side of the bets are going on as to how those earnings will
look. Now this is Nvidia. N-V-D-A. And one thing about Nvidia here is their
earnings are coming up in a couple of weeks. They are forecasting that their
earnings will be very strong and so first thing the markets do is they say
okay we're going to price based upon what they're saying and then as the
earnings date when they make their announcement of what they actually were
for the quarter then the rumors start. Well they'll be below what they estimate
or they'll be above what they estimate. So that'll drive the markets up to the
point where the earnings call happens. And here you can see Nvidia is a
stupidly expensive stock. $730 per share. Which puts it, I mean yeah if you want to
buy a round lot, a hundred of them, you can but I mean that's going to cost you a
lot. Even one share is awfully rich for most people in this class,
including me. But you notice that it is up about 1.15%
for the day. In other words the rumors are that the earnings will come in
better than what Nvidia is saying they will. Now if you look down here real
quick you can see a quick chart of earnings. You notice that Nvidia has been
beating its earnings forecasts for the last year. Every for each quarter of last
year. When it says well our earnings will be here for example the last one.
They'll be a little better than $2 a share. Well they came in quite a bit
better than $2 a share. So now the same happened here with this quarter. They
the company said we are we think our earnings will be about $3.40 a share.
Well when they came in they were $4 a share. So that gives the market this
feeling that the company is conservative in forecasting its earnings. So here we
come on February, oh that's the 21st, it's not quite, well that's a week from now.
I'm sorry that's a week from now. So Nvidia is saying our earnings are going
to be at about $4.50 a share. And if you're looking at this the market is
pushing it up a little it was pushing up saying okay we think that it will
probably be a little better than $4.50 a share. We're going to buy in. Now here's
the rule and I said this on Monday and I'll say it again. There's an old rule in
investing what this kind of investing. Buy on the rumor, sell on the news. In
other words right now the rumors are that Nvidia is going to come in with a
very strong stronger than their estimate earnings for the previous quarter. And so
it's going up. So you see buying on the rumor. Now when the company comes out
with well our earnings were well suppose they are better than normal. That's not
going to move the stock at all. So you sell on the news. If they come in worse
you get out of there before they make the earnings call. Any way you cut it it's
smarter to get out when the news is about to happen on what really
what the earnings really were. So right now you see the market buying. Let's
look back here about five days. It's kind of pushing itself upward
here. It had a big spike when there were rumors that they were going to come in
substantially above 450 and maybe about 474 80. So that was where the main part
of the rumor was turned into action by investors. They bought there on
the spike of the rumor. Now there is more belief. Sorry about that. Try that again
five day. Now there's rumors that maybe it'll be a little better than we
expected and so it's still climbing. It's doing pretty good for the time being.
Now what's going to happen? It's hard to say but right now there's positive
sentiment about Nvidia. If you look at the numbers though the beta is 1.68.
That is a very risky investment. So even if you were to say buy on the rumor
you're buying on very risky rumors. This company is fickle. It can burn you.
Either way it can take you down. The PE ratio is telling us that it is
substantially overvalued. So any price run-up in this is going to be temporary.
Eventually it will find its way back down toward intrinsic value at a PE ratio
of about 30. So that's how you think about this. Now you see Nvidia is a
profitable company. EPS earnings per share which we covered last week in
ratios is 7.58 or actually on one Monday we did this. So $7.58 a share.
That's a really healthy company but notice this the dividend is really small.
In other words this company takes most of what profit it makes and plows it
back into the company's operations. In other words a rough way to think about
the company made that belongs to the shareholders $7.58 per share.
Now they are giving back to those shareholders only 16 cents of that. So
the remaining $7.42 they're turning right back into the company.
That's risky. I mean if you're an investor getting a dividend check is
very low risk but thinking the company can throw your money back
into the company instead of getting it to you as a dividend and that money is
going to turn into a great deal more money. Well that's when you take risk. This
company has a very low dividend that it pays 0.02% of the price you're
paying for the stock so it's almost virtually no dividend. You're betting on
this stock continuing to rise for the foreseeable future but when you see that
the PE ratio is already well above what would be intrinsic value of the price
well that's risky as all get out. That's a very risky stock. Something that you
might be tempted to jump into but you might be sorry when you did it.
Okay I don't know it's hard to say what else to look out. Well one quick thing if
I'm not mistaken alphabet which is what we call Google up barely today very very
little activity. In other words it's acting like the mark overall market is
acting. Very sluggish bullish yeah but not some spectacular bull run. On the
other hand you look at a company like Tesla TSLA which has a very high beta
and it is up the stock market is up a little and with a high beta that would
tend on an average to mean that the stock is going to go up by a magnifier
of it and sure enough it is it's going up today but it's still not a
spectacular thing it's still kind of like a grind upward but it is a it is an
upward trend. So that's how you look at all these. Now let me get down to the
lecture and I've said a little about this on Monday and a couple of other
lectures too but long ago back a well before your time and we did these
present value future value with formulas on paper and maybe we had real real
sluggish old old calculators or we use slide rules which were a mechanical
device for doing multiplications and divisions but then came along in 1975 I
think it was Texas Instruments came out with one of the first consumer level
slide rule calculator it was a scientific calculator and it was
something it was just appalling the things that it could do that we used to
do by hand or using tables. Few years later back in the early 80s I think it
was financial calculators started showing up the cream of the crop at the
time was one by Hewlett Packard the HP 12 C I'm telling you all this to explain
why we're going to do it the way we're doing it the way we are now but back
then the HP 12 C was like in all the big wigs all the traders all the corporate
finance people got their hands on HP 12 C's the only downside of them was they
didn't use algebra algebraic notation they didn't say you didn't put in five
times two equals they use another system called reverse polish notation RPN so
you would put in five enter four times and that's either here or there Texas
Instruments came out a while in the same era in competition with some low-end
business calculators like the BA series and they actually did things like
present values future values and it was kind of a revolution but it was kind of
cumbersome they had a one-line display and it was you had a little skill it's
still around and some people still use it in fact I if the book is still doing
it like they did in the last edition which is the one that I've been using
until I got my new edition they actually show you how to do these problems on a
BA 2 a Texas Instruments BA 2 but then came along something a little later the
Texas Instruments TI 80 series 80 they 0 the 8 to the 8 3 and 8 3 plus the 84
these had an actual set of dedicated functions they called them apps and you
hit apps and then they gave you what different ones and you went to the
finance and lo and behold the about anything you could want to do bond
mortgage payments present values future values effective interest rates and that
was the standard but of course in colleges they weren't going to have
anything to do with that they still wanted students to use either calculator
basic calculators with but usually with tables you use tables in a class in your
in your accounting classes those are the same tables that have been around for oh
actually more than a century it's an old technology really old just you go to the
table and find a factor and you multiply that by the amount of money and there
you've got an answer but it's still cumbersome it's ancient but it's still
used and then along came well then a few professors started saying no we're going
to do these with those financial calculators this is ridiculous and even
as much as recently as two years ago I was taking flack because I was saying
we're using calculators we're not going to do this with tables and with formulas
we're going to use calculators so of course that was an outrage and they they
tried to hang me for that but then came excel but its predecessors had been
around and some were using its predecessor the first one was CP slash M
and then came along super calc then Lotus one two three then quattro and
then excel but god forbid I should use excel to teach you how to do these
finance problems and of course you can tell how much I care about that you're
going to use excel to do most of your work in here now don't get me wrong
there are times when a financial calculator can actually do it a little
bit faster than excel because it's excel is laid out for many many different
things and these the financial apps they they are right there just to do one
thing and one thing only finance I'm going to show you something here now one
more piece of the story is this the Texas it's with TI-83 there Texas
instruments actually created and kind of made available to geeks like me and
others a virtual TI-83 calculator it was it comes up on your computer it looks
like a real one it functions like a real one it's just like you have in fact it
even turns off after a minute if you don't use it for some reason to save
battery or whatever but it was out there and it was available through the 90s I
was I was using it but then TI did Texas instruments it kind of disappeared from
their website some years later what behold it showed up at Google in a Google
site run by Google and then about five years ago it what they locked it down so
you couldn't get to it well you see I actually still had my old floppy disks
that had the original virtual TI I'm going to show you something I've made it
available so that you can download it now if you go posting this on social
media I will hunt you down but here it is the warning is it works only on PCs
because PCs Macs are not used in finance they're just not there as a matter of
fact scientific subject matter research calculations Macs just aren't built for
that so it's only available if you have a PC let me show it to you you go into
your files okay this is what you'll see okay files right here now follow the
follow the instructions so you can see how this is done files and if you go
clear down to the bottom of the top level of the files you'll get the very
last file you see is virtual TI-83 graphing calculator you see it and this
is in you'll be able to do this but you have to follow what I'm going to do here
step-by-step first thing you download it now the next thing is you're going to go
and find this file it'll be in your downloads
download there it is virtual TI-83 calculator now this is a zip file so
you're going to have to right-click and well this didn't work in my first class
try to yeah they've made it so that the just double clicking won't extract it
but you can just go like this right click show more options seven zip so
extract the files that way with a right click and go to more options you'll see
extract the files and there it will come up
so what you're going to do is you're going to you can leave this in downloads
if you want you're going to extract it just extract it to the downloads okay
and you say okay now it will extract a folder of the same name now you can put
this leave it where it is you might want to put it someplace else because if you
if you're like me you usually clear out your downloads you delete your downloads
after a few days so I usually just take this over and I put it in my documents
well that worked as like a frickin charm oh there it is
well let's try that again documents there we go I screwed up there
documents there it is now in here you double click and you'll have to double
click you'll double click and get to a folder VTI 83 go down one more level
there's the calculator the one that is the blue icon don't just leave it there
right-click and then go down to more options and send it to your desktop
that way the calculator will always be right on your desktop where you need it
the most now you can't see the desk really let me do this this is what it
will look like on your desktop and that way you can bring it up whenever you
want I you could leave it in double go into documents every time you wanted to
bring it up but it's nicer to have it on your desktop watch it's doing those
look at that there's your calculator okay it's a real one it does everything
that the real one does it never runs out of battery and it's always there for you
you don't have to search around in your bookbag for it it's right there on your
laptop or whatever now I'll just show you this very quickly once in a while I
might we'll do this in Excel and then I'll say well let's see if it in the TI
like I said sometimes this calculator it's more efficient to do it here the
downside though is that if you do finance calculations on the calculator
you don't have any documentation of it with an Excel spreadsheet you've got it
you can print it you can email it to people here it's just for you to be able
to do something if you do apps and finance number one enter you've got all
of these anything almost anything that you could possibly want for a class like
this is there somewhere and they just like for example and I'm sneaking
something in on you time value of money solver now you don't have to know this
don't type this for God's sake but let's say we want the how much you would have
your monthly payments would be on a car okay we're going to get a five-year loan
with 12 payments per month 12 payments a year so that would be 60 payments every
year well let's say that the APR on the loan is seven point nine nine percent
that's annual so you have to divide it by 12 to get months and I'll teach you
how to do all this now the price value the present value on almost any financial
calculator you'll ever use present values come out as negatives and you
enter them as negatives so let's say that you decide you want to buy a
twenty eight thousand dollar car so I would put in for the PV negative 28
thousand try that again 28,000 and I'm going to skip by that I'm going to leave
everything else alone the payments are at the end of every month you don't play
with fees no matter what you were told by other clay in other classes future
value you're not going to pay any kicker at the end so I just take it back up
here to PMT and then I say alpha solve and there's your monthly payments that
fast this is actually more efficient if you remember how to put in each of the
entries this is faster than Excel because you're going to have to do the
setup of each of the parameters and then plug them in remember what function it
is and all that this and there are so many other kinds of problems that you
could do let me do another one okay let's say that for the next 15 years I'm
going to put money into an account that pays five point two five percent
compounded quarterly divide by four and then I'm going to say whoops so that
means that this would be 15 times four quarters you always have to make account
of the compounding period and the payments that let's say that I decided
that I am going to want to make payments into that of every quarter I'm going to
put in $500 and I have no present value I'm not going to put it in any extra at
the beginning
so that's a zero now in this case I'm going to put in the payments at the
beginning of every quarter so how much will I have after 15 years of doing this
that was I said 15 years yeah let me do 15 times 4 and it's a lot easier to fix
it here so let's see how much I'll make my last payment and one quarter after
that I'll take the money out let's see how much I'm taking out alpha so
forty five thousand eight hundred dollars this is incredibly faster and
more efficient than Excel but Excel is how we do things and Excel you will have
a paper trail electronic or printed if you wish so even though this does
lightning fast once you get the hang of it it's just sort of like a mini
language it works awfully fast that's all there is to it so I won't hate on
you if you want to use a calculator either a physical calculator or this
virtual TI-83 I won't hate on you but you do have to we do have to know the
the Excel version to help you with that I have already created a bunch of
templates now we're going to build these templates together so you see how they
work and see where you have to put things in but in Excel let me do this
student view so in your files you go down here to your spreadsheets and you
will have a whole bunch of different templates for different major problem
groups like bond calculations like free cash flow analysis like internal rates
of return and loan payments and net present values and internal rates of
return present value and future value we'll have templates to do these your
job is to master the Excel and then to make those templates your own so that
they can do this which we did a century ago on paper then we did with tables
then we did with calculators and then somewhere along the line we finally came
to Excel and that's where we are now we can't be too comfortable here because
Excel is evolving rapidly it'll still be around for several decades but it's
beginning to be augmented first by Python it's augmenting it and then
within a year easily artificial intelligence will also jump in too I've
already connected some one chat GPT to Excel so the GPT goes over and creates
models in Excel for me to use and so but I'm trying to keep you as close to the
frontier as I can and right now the frontier is Excel so these are here for
you and we will go through each of them I you might even want to download and
look at them and see if you can figure out how what happens I've tried to
color code them so that you know where something needs to be put in and what
you leave alone and where your results come out matter of fact let me how does
this one look up I don't I always do that let me do look at the present the
ones today seriously
now these are for annuities but you can use those these for lump sums as well
and you can see how I set them up there's cut they are color coded don't
touch anything here put in the white spaces you put things that you get from
problems and all that this is just taking you on a quick tour of what I've
created for you to do these with this in one way yes it does make you weaker
because you don't know the formulas and you can't do things the way we did back
in the neolithic period but in a way it makes you a lot stronger and so we have
to leave some things behind as we accelerate into the future and that's
where we are at least in my classes as long as you're in my class I'm right okay
enough of that let me go back let me get out of this for a while now I want to
point out one thing here sometimes a problem is in what we're doing right now
a problem is so easy the formula is so lightweight that it's better not to use
Excel at all and even the calculator you use just use as your dumb monkey in
doing them but I start this and I do appreciate that you were shown this in
your accounting classes and that's why I have to do it again so that you learn
how to do it from a finance person let me do it you came to me sir and you
decided I you told me I want to borrow $20 from you for a year and I did the
old intermediation of the level the timing and the risk okay yeah I'm gonna
give you a $20 that that that day and of and you say that is sweet brah I mean
I'll give you the $20 back one year from today and I say you kiss my wrinkled old
ass you will what's wrong with him giving back that money right now madam
give me it back to me in a year my $20 is going to give back to me in a year
will you get away from that wallet dude what's wrong with that well I said it's
a year's okay I mean it's a year's okay but he's going to give me my $20 back
yeah well that there's that's exactly right but we can even ignore
inflation eroding purchasing power we can erode risk factors and all that
there's something basic you see I am I don't have this $20 for a year that
means in for a year I cannot use that $20 to buy a grand slam breakfast at
Denny's on their happy meal menu and a piece of pie afterwards I have foregone
consumption I have given it up for a year so I want he has to offer me some
compensation for the opportunity cost of foregone consumption that's not
inflation eroding purchasing power that's nothing but the fact that I don't
get my grand slam happy meal and my piece of apple pie and my coffee for a
year that's the problem you see that's how Western capitalism works you give up
something you get something for giving it up and that is what we call an
interest rate that's what we call it it's an interest rate that's what its
function though there you'll see later in the course interest rates have a lot of
different parts to them but at the core of every interest rate is a reward for
for giving up consumption the opportunity cost of foregone consumption
that's what an interest rate is and another thing about an interest rate well
two other things one is that the interest rate has different names they're really
all interest rates we can call it a yield a compounding rate a discount rate
we can call it some other things but it's they're all interest rates now the
interest rate that I will charge you is not a price it's a rental rate a rental
rate for money it's the rental rate so it's like a wage rate it's like anything
else when you get a when you get a job yeah I've been telling you get a job for
a long time get a job man no but when you are working a job I hired you I
didn't buy you that's seven dollars and twenty five in your case four dollars an
hour that is that is not a price I am just renting you for for whatever I I
need okay that's the whole point of understanding that these are just rental
rates it's like real estate rental rate of property or something like that a
wage rate rental rate of labor and human capital the interest rates are just a
rental rate of money or capital in one one or the other so taking all of that
into account we begin the journey and I do this in a way of warning you that for
many years I was a math teacher both at the Ohio State University and in a K
through 12 school where the kids like me but the administrators were really
scared of me but or didn't like me so let me start it out and hear me out
about this somewhere in your dark past
you learn conversions unit conversions one centimeter equals 2.54 a one inch
equals 2.54 centimeters one foot equals three yards now what we do with present
values and future values is we are doing unit conversion that's all we're doing
the difference is that these are what are called static conversions they're
the same in any situation if you're if the units are the same the conversion
rate is the same and it's true at any given time period any given place
anywhere in the universe you're going to fly to Alpha Centauri and your co-pilot
is going to say well how far have we gone well we've gone 1 billion
centimeters and he says no dude I wanted in inches come on man we're English we
use the English system so it would be the same there in 200 years but with
money it's not a static conversion it has things that would be different
depending upon actually two parameters and I'll get into that in just a minute
again as a matter of fact those tables that you had in your accounting courses
to find present values and future values those were unit conversions no one
probably ever told you that but that's all they were they're just unit
conversions based upon the interest rate and the time period the interest rates
across the time I think that was with it interest rates across the top the time
period down the column or maybe was the other way around but those were nothing
but unit conversions but as you could see from those monster tables those
ridiculous tables they were not static you couldn't just look at the same
place every time so what I'm going to do is I'm going to write a formula the
for this is actually the core formula of all of the time value of my of all time
value of money problems the future value of a lump sum of money future value of a
lump sum now this formula is so basic that you you might want not want to use
a Excel at all for something like this just set it up and key the numbers into
the calculator but the future value is the current value what we call the
present value times 1 plus the disk the interest rate and that quantity to the
t-power this is where you have to watch yourself because the R is the periodic
rate and the t is the number of periods
so the periodic rate so let's say that we had 8% APR annual and the t let's say
the t let's say that the t is why I don't know five years see these are both
in years annual percentage rate number of years so let's take an APR of 8% so
the periodic rate and over here the number of periods over here are so
let's say that we had number of periods that would be for let's say the number
of periods was 1 so in that case you would have 8% divided by 1 which would
be 8% and that's what you would put in there 8% 8 divided by 1 the number of
periods would be 5 times 1 so the number of periods would be 5 so you would put a
5 there let's say that the number of periods was 2 semi-annual compounding in
this case R would be 8% divided by 2 which is 4% and the number of periods
would be 5 times 2 or 10 periods so in the art you would put 4% and in the t
you would put 10 let's try quarterly 8% divided by 4 quarterly is 4 in that case
your so your so your R would be 4 and your number of periods would be 5 times
4 there would be 20 quarters in a year those would be the numbers you put in
now a very popular one is monthly that's how you most consumer loans have
monthly payments so the compound is automatically monthly in that case you'd
have 8% divided by 12 which would be 0.67 percent and the number of periods
would be 5 times 12 or 60 months in five years. Now the next one suppose that the
compounding is weekly what would be what would you multiply the interest rate or
divide the interest rate by weekly 52 you'd be surprised at how many people
don't know that in my last class I got 54
8% divided by 52 for weekly and your number of periods would be 5 times 52
which is I'm not even going to try how you did that in your head hell okay the
next one minute lay no no no no don't don't don't yeah there is yeah minute
lay and there's actually even if you have massive amounts of money a bank may
give you instantaneous compounding and it doesn't even follow that simple
division you have to use the natural constant e to the R or to the negative R
it's weird but anyway okay enough of that but now a little side note here the
prefix by bi that means that it's every other so if I said bi weekly that'd be
26 bi monthly every two months that'd be six and then there's the semi you see it
there semi annual means twice a year semi weekly would would it gets a little
bit more complicated so I wouldn't do that semi annual is normal but the by
you here well you're paid bi weekly and in that case that means that you get a
paycheck every two weeks and that's actually very common in some companies
and industries to pay bi weekly so I won't throw that one at you but just
know the 1 2 4 12 52 and those will get you through well let's play into practice
I died and you were my son and I'm bequeathing to you $250,000 I'm not dead
yet I've just told you about this $250,000 so of course the first thing you
do is go look up how to kill your dad but as it turns out now I actuarially I
will live to 83 years of age now don't believe that stuff about 77 or whatever
it is right now life probabilities don't work really like that if you live to a
certain age you will live a certain number of years past that so if I live
for example if I live if I'm 65 there's a very high probability that I will live
to be 83 years old so let's take that as a basis here
you
will inherit
$250,000 in 18 years
how much is that worth now if the discount rate
is 7.4 percent compounded quarterly now over here I'm going to do another
problem where you put $15,000 in the bank now
you put $15,000 in the bank in a bank account
that pays 5.75 percent compounded monthly
how much will you have in 15 years these are two opposite sides of the same coin
let me explain you see in that second problem in that second problem I am
trying to find a value in the future so that formula is what I need but the that
first problem over there that's I need to know a present value how much
something is worth now so I have to take this formula and for that one I have to
rearrange this formula so that I get the present value and that will be the
future value divided by 1 plus R to the T so this is the future value formula
this is the present value formula and those two are the foundation of all of
the other formulas they might look a lot more complicated but they really all are
derived from that one little thing about this present value formula you'll
oftentimes see me write that as instead of future value divided by 1 plus R to
the T you'll see me write it as future value times 1 plus R to the negative T
from your high school algebra the reciprocal of the denominator to a power
is the multiplication of that denominator by the negative of the power
now why do I do this it's practical dividing by a complicated set of numbers
calculation you are more likely to make a mistake in it that you could do it
with the second line there but you'll see me usually do it by the third line
just run it as multiplications instead of trying to remember how many
parentheses you put in in a denominator and I am all forever getting that wrong
so in other words for the second problem I did where you put $15,000 in the bank I
will need to find out the future value and that would be the first formula
there it's the present value 15,000 times 1 plus the R 0.0575 divided by
monthly 12 and then you raise that to how many years did we have the 15 times 12
here's where you got to watch it that that exponent you've got to put it in
parentheses otherwise the calculator will take the power as 15 and then
multiply the result by 12 let me show you and I'll just do it on this TI since
I've got it up here where you can see it do you see this this calculator turns
off after a minute why why would the calculator turn off to save battery okay
let me get out of this by the way the way you get out of the apps second quit
okay
cranking it along here I'm going to take 15,000 times open parentheses 1 plus
0.0575 close the parentheses and then raise it to the open parentheses 15 times
12 oh I screwed up did you see what I did there I didn't even look at my own
formula divided by 0.0575 divided by 12 close the parentheses and then raise
that to the 15 open parentheses 15 times 12 so let me repeat that for the podcast
15,000 times open parentheses 1 plus 0.0575 divided by 12 close the
parentheses to the power open parentheses 15 times 12 close parentheses
a caution here if you are doing just formula math on a calculator or you're
using Excel you use the decimal per version if you are in the apps on a
financial calculator including this one you don't turn it into a decimal you key
it in as the percent so if I were in the apps here I would have put point 0.0575 I
would have just typed in 5.75 all financial calculators do that they take
it as a percent Excel doesn't the normal front end of any calculator
scientific calculator or other calculator doesn't do it but anyway
survey says hit enter $35,463
I'm a little worried about that here real quick
don't worry about what if the book says rounded two decimal places yeah but when
we do these in my in my book the dollar just rounded to the dollar and if you're
on a quiz or an exam I give you a couple of dollars leeway either way and it just
in case you had a little bit of a finger fart or something when you were keying
something in the next question is does this make sense the answer if you've
done something major wrong a wrong place a division is that a multiplication
or something like that finance problems will either blow up the answer or turn
it into little pennies if you get a number that kind of makes sense well you
probably got it right so that's a comforting thing now let me do the other
one here for that one we're going to use the future value the present values
$250,000 times 1 plus in this case it will be point zero seven four divided by
four quarterly to the negative how many years whether 18 years times four
quarters per year so in that one 250,000 times open parentheses one plus point
zero seven four divided by twelve close the parenthesis and then you raise that
now open parenthesis why do I do this why don't they put me in a home you know
give me a tray of food every day and you know maybe let me play on the shuffle
board and take my metamucil open parenthesis now here one thing I want
mention here oh let me try that again really 24,000 250,000 times open
parenthesis whoa boy if I had a dog I'd like this I'd shoot him plus point zero
seven four divided by four close the parenthesis and then raise that one point here put a
negative right here you don't use the minus use the negative and you put that
18 times four close the parenthesis and you get an answer sixty six thousand
seven hundred ninety five dollars and everything else will put we'll do an
Excel on Monday right now you have a quiz to take once you're finished with a
quiz that's all I have for you today I thank you