TI BAII Plus Basics for the CFA Exam (2024)

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Video Transcription

Now, there are two calculators that are permitted for the CFA exam. One of them is the HP-12c, the Hewlett-Packard, and then there’s an addition to that called the Platinum Edition, I believe, which is essentially the same in functionality.\n And also, this TI calculator.

If you are new to the financial calculator or a lot of the functions, we really suggest that you get the Texas Instruments calculator. We focus on that—it’s more intuitive. I’ve found over my years of teaching it’s\n easier for students to use and can catch on to.

So, our examples in the SchweserNotes, although we have some for the HP\n for specific functions, most of our answers and explanations and examples are based on the Texas Instruments calculator.

Now there’s a plastic one, and then there’s this one called the Professional Edition. So, since I’m a professional, Schweser bought me this one some years back. And it has little rubber feet on it. It’s a little\n heavier, has a better feel, and the buttons feel cooler when you press them.

In terms of functionality, there are a couple of functions that are on this Professional Edition that aren’t on the other one. Neither of them is very expensive. And as far as I know, they last forever. And never had trouble with\n one, never replaced the battery. Although I guess, it could happen if you were using it all the time. Mostly, we use Excel these days, so they don’t get used all that much. But you need to be familiar with it for the exam.

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Setting up the TI BAII Plus

So, let’s first talk about setting up your calculator. Now, there are 2nd functions to a lot of these keys, and you’ll see what’s written over the actual key itself. Across the top row, you see it says QUIT, SET, DELETE,\n INSERT, and all that sort of stuff. And those are the 2nd functions.

Setting the Number of Decimals

So first off, we want to set the number of decimals. I set mine to four. The reason I do that is if I get a four-place decimal, then I’m getting what? Two places in percent, right? If I get.0522, I know I’ve got 5.22%.

So, my accuracy or my precision, I should say, is to 1/100th of a percent. One basis point. And that’s usually, I think, adequate for anything you’re going to face on the exam.

Now the calculator itself is carrying, I forget, seven, eight, nine, digits in its brain, and they’re always there. You’re not changing or rounding anything except what’s in the display. So if you’re using four\n decimal places, and you get to a problem where for some reason you need the 5th and 6th decimal place, you can just go times 100, it’ll move that over, it’ll move the decimal point, but you’ll see those next two\n digits just that easily.

So use that 2nd key and find the format key. That’s the 2nd function for the decimal point in the middle of the bottom row. And if I do that, mine reads DEC equals four. If you want something else in there than what you have,\n then put it in; put four in, for example, and then press ENTER, and then you can clear the display, and that’s how it’s going to display all the time after that.

Setting Payments to the End of the Period

Next, we need to set payments to the end of the period. I think that’s the default on the calculator when it’s new, although I’m not sure. It’s been a while since I had a new one. But use that 2nd key and then\n the BEGIN key.

Now, that is right above the PAYMENT key in the third row. So, if I go second and then hit that PAYMENT key, mine says N, so I’m not going to change it. If yours says BEGIN, then press second, and then press that SET button.\n It’s actually the ENTER button in the upper-left corner there, and that’ll toggle between beginning and end.

When it’s in begin mode, there’s a little BGN that shows up in the upper right-hand corner here and lets you know you’re in begin mode. If it’s in end mode, since that’s the default, there’s no indication\n of that on the display. So, what you’re essentially telling it, well, there are four payments in this annuity, a little short four-payment annuity.

In end mode, it assumes those payments, deposits into the account, or payments out of the account, are made at the end of each of the next four years or periods. If you put it in begin mode, it assumes that each payment comes at the\n beginning of those periods. So, the first payment would come today, which is the beginning of the first year or first period.

Setting the Number of Payments Per Period

Now we need to set up the number of payments per period. I think you should set it to one and just leave it there. If it turns out to be a monthly payment, we’ll use the monthly interest rate. And N will be the number of months.\n

If it's quarterly, why, we’ll use a quarterly interest rate. N will be the number of quarters. Our payment will be payment per quarter. So, really it says I/Y, but think of it as payments per period, and then we’ll just\n think in terms of whatever periods we have in the problem we have to deal with. So use the second key and then hit I/Y. The display will read payments per year or payments per period equals, then press one, ENTER, and then you\n can clear the display again.

Setting Modes of Operation: CHN vs AOS

Now there are two modes of operation. One is CHN, which I assume stands for chain mode, and AOS, which has to do with the order of algebraic operators. Now, take a look at this calculation here.

And let me find my magic teaching pen here. I’ll underline this. We’re looking at this right here. And so you understand the difference between these two…just look at the different answers you would get.

Now, if we put in 3 plus 5 times 4…so this is what we’re putting in. I’m not putting in any of the parentheses. So, if I just put in 3 plus 5, when I hit times, that also does an equal function in chain mode. So,\n 3 plus 5 is 8, I hit the times, and then you’ll see 8 in the display, enter 4, enter equal, and you’ll get 32.

Now, if you are set to algebraic operations priorities, then it goes 3 plus 5 times 4. Well, the order of algebraic operations, if I remember, is exponents first, then multiplication and division, and then addition and subtraction.\n So since this times multiplication operator takes precedence, it multiplies 5 times 4 and then adds 3, so we will get 23.

Now, there are parentheses on this. In the middle there, you can see the left parentheses and the right parentheses, so even if you are set in chain mode, you can insert your own parentheses. So if I did 3 plus…well, if\n I were in chain mode, and entered this with the parentheses, then I’d get 23. And when you close those parentheses, you have to hit the equal sign after that. Closing the parentheses would give you this value, 20, and\n then the equal sign would get you to 23.

And you change those with that same format. If I go to the second format, I get my decimal. But I think if I do an up arrow, mine says CHN, which is where I want it. If you want it somewhere else, if you want it in algebraic operator\n mode, then press 2nd, and press that SET key, the Enter key, and that’ll toggle between Chain and AOS modes.

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The √x, x2, 1/x, and +/– TI BAII Plus Keys

So once we’ve got our calculator set up, now let’s take a look at some of the keys on there. The reason I’ve got these four keys separated out here is that these keys all operate on the number in the display before\n it does anything with it. And I’ll show you an example of that.

Now, the usage of these is straightforward. If I put in 100 and then press that square root of x, it displays 10. Five and then I hit x squared, I get 25. If I hit the 1/X key, it gives me the reciprocal of that, so 5 1/X key\n gives you 1/5 displayed as a decimal as 0.2.

And then, so, those are all right across the fourth row there, and then at the bottom right, we have the plus-minus key, which just changes the sign of whatever is in the display.

So, if we want to multiply times minus 5, then we put in 5, hit the minus sign, and then hit the times sign. It’ll be a multiplication sign. It’ll be multiplied by that number in the display, minus 5.

Let’s take a look at an example here. And you can see here that these keys operate on the number, and then it moves on. So look at that first example.

If I want 0.89 divided by the square root of 2.17 times 7.3 squared, I just have to enter 0.89, then divide by 2.17. But before it divides, that's the important point here, and it’s really handy. Before it divides,\n it’ll take the square root of that. And then when I hit the multiplication, it’s multiplying that, the square root…dividing by the square root of 2.17. And then times, I hit 7.3, but I want to square\n that, so I do that, and then hit equals, and so it multiplies by that, 7.3 squared.

Now, we could do this a different way. Sometimes when there are a lot of things going on in the denominator, it’s easier to punch it in by doing the denominator first. So that’s what I’m illustrating here.\n I can put in 2.17, take the square root of that, and then hit the 1/X key, and then multiply by 0.89. Well, there's not much difference in work here, but imagine if you had a denominator that was 1.12 to the 7th power.\n Then it would be easiest to do 1.72 y to the x will take it to the 7th power, then hit the 1/X key, and then multiply by 0.89 or whatever’s in the numerator.

So, that’s just a handy trick. I think one thing you want to try and avoid is writing down any interim results. When you write down an interim result, and then have to put it back in the calculator, there’s\n always a chance for exam-taking error, dyslexia to take over, or whatever gremlins are in your head at the time. So the less you do that, the less chance there is for making mistakes.

So, I try to do the calculations all kind of in a row within the calculator. If you have to save something, we’ll talk about saving something in the memory function here in just a bit. So, for 2 times minus 3.5, 2\n times 3.5, change the sign to minus 3.5 and then equals to get the answer of minus 7. So a little bit of practice and you’ll be very comfortable with these.

TI BAII Plus Exponents yx

Okay, I mentioned taking something to the 7th power. We can’t do that with the x-squared key. With the x squared key, you can get x squared. If you press it twice, you can get X to the 4th. If you press it three times,\n you can get X to the 8th. But for these other exponents, we’re going to have to use the y to the x key.

So, here’s our example. We want to calculate 1.75 to the 5th power. So, we enter 1.75 and then hit that y to the x key, it’s just above the 9. And so, you hit the y to the x key, hit the 5, and then hit\n equal, and that’s what it gives you. It gives you 1.75 to the 5th power. So, here’s an example of how we might use that. The example here says, “A firm’s dividends have increased from $2.21\n to $3.54 over the last four years.

Calculate the annual compound growth rate of dividends over the period.” Well, first, if we’re going to say, “Well, we’ve got four periods of growth,” then we’re going to use the\n one-quarter power here. We’re going to take the 4th root.

So, 3.54 divided by 2.21, we want to take that to the 1/4 power. So what we could enter is y to the x, then enter 4, then enter 1/X. Your display will change to 0.25, which is what 1/4 is. And then hit equal, and we\n need to subtract 1, but we can find out that four periods of compound growth of 12.5% would get us from $2.21 to $3.54.

Now, if it’s pretty obvious what that fractional exponent is, as in this case, we know that 1/4 is 0.25, we could go 3.54 divided by 2.21, hit the y to the x key, put in 0.25, hit equals, subtract 1, and get 12.5%\n rate of compound growth that way. So, that’s pretty easy with 1/4 or 1/5. Even with 1/3, you can put in 0.3333333, but if it’s 1/7 or something like that, or to the 1/7 power, it’s just as easy\n to put in 7, hit that 1/X key, and get the decimal equivalent of 1/7.

Storing and Retrieving Results on TI BAII Plus

Now, storing and retrieving results, you’ve got ten memory registers on this, and we’re going to store them using the STO function, the store key, and retrieve them using the recall key. And so every one\n of those digits on your keypad, 0 through 9, identifies a different storage register.

So, for example, this is a problem derived from the dividend discount model, the constant growth model. And so, what we’re going to do here is do it in pieces. We’re going to take that first piece and go\n 1 divided by 1.13 equals, and then hit the store, and then 1. And that stores that in register one.

So, for example, this is a problem derived from the dividend discount model, the constant growth model. And so, what we’re going to do here is do it in pieces. We’re going to take that first piece and go 1 divided by 1.13 equals, and then hit the store, and then 1. And that stores that in register one.

The next piece we want to do here is 1.1 divided by 1.13 squared. So, now we’re going to use that squared function right in line, hit equal, that’ll give you your answer, and then store that in the second register,\n and we’ll store that answer of 0.8615.

For this third term here, I use the parentheses because remember, I’ve got this in chain mode. And so, I want to take 1.21 and then I want to divide that by 0.13 minus 0.05, 13% minus 5%. And then I want to divide\n that by 1.13 squared. And when I get that, I can store that in register 3 by hitting the store key, hitting the number 3, and that will store 11.8451.

Just as an aside, you notice that 1.21 divided by 0.13 minus 0.05, another way to do that in chain mode is to go…0.13 minus 0.05, and then hit equals…get 0.08, and then hit that 1/X key, and then multiply\n that 1.21, and then we can get that answer that way as well. And then we’d have to divide by 1.13 squared.

So, once we’ve got all these pieces, then we can just do, we’ve got in our display, that third one. We’ve got 11.8451 displayed even though we’ve stored it. And then we can just go plus recall 2,\n plus recall 1, equals, and come up with 13.5915.

Now one reason you might want to do problems like that is, say, you’re taking a multiple-choice test, and you get done with a calculation like this, and you look down, and there are no answer choices there that match\n yours to any significant degree. Well, now, you’ve got to troubleshoot this and find out where the error is.

Well, if you did it all as a single calculation, you just have to start over. If you’ve got the pieces stored in three registers, you can check each piece against what you’ve got stored. When you find one that\n isn’t right, then store the new value and go plus recall one, plus recall the other one, and then get your answer. And hopefully, by then you’ll find one that’s one of the choices for that problem.

Now, the second memory function shows the value in memory register 0, and then you can use the arrow keys to go through all of those. So that MEM is actually the 0 key, so I’m going to go 2nd function, hit MEM, and\n it says M0, memory and register 0, and then use the up arrows to go to 9 or the down arrows to take them numerically, M1, M2, M3, M4, right on through.

Now you can clear all these registers by doing 2nd, and then hitting clear work, which is that second function of the lower left-hand key down there. Now I’ve got Y there because I don’t know why you’d\n ever have to change them. As soon as you put something new into a register, it just overwrites whatever was in there before. So I’ve never had occasion to clear them, but you can if you like.

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TI BAII Plus Combinations

Okay, the next function we want to look at on this calculator is combinations. So, the idea of combinations is in this example.

How many different pairs can be made from the letters A, B, and C?

Well, there should be three different pairs that we can make from that. And so that’s a simple example. It, of course, gets more difficult as, I say, how many pairs are there in 17 or something like that. But\n this nCr function, which is above the 2nd function above the plus key on the right-hand side there, that answers this question…uses the formula.

This is one place in which the Texas Instruments calculator has a function that the HP does not.

So, we just go three, and then hit that second function and then the plus key to get that nCr, and then put in two. So you’ve really asked the calculator, “How many groups of two can I pull from an overall\n group of size three?” and that will display three, and those are our three pairs.

Now, notice we don’t count AB and BA separately when we’re using the nCr, the combination function is there. So, let’s look at a different question. How many different pairs are there in four items?\n Well, if we enter four, take that nCr function, two equals, that gives us the answer of six.

Permutations

Now, when order does actually matter, then we’re talking about permutations. So, now we’re going to count AB and BA as two different pairs when we talk about permutations.

Because with permutations, the order matters. Well, understand you’re going to get a bigger number with permutations than with combinations because we are double-counting each pair here in reversed order.

Time Value of Money Keys on TI BAII Plus

Now let’s look at our time value of money keys. You’ll use these quite a bit. They’re in that third row there, and you see that there’s five of them. And really the logic of it’s pretty straightforward.

If you put in any of those four values, and then you press on the fifth one and press compute, it’ll calculate it for you based on those values you put in for the other four.

Now, sometimes, as a shortcut, people hit this clear time value of money, and that’s out there above the FV, future value key, it’s the second function of that.

Now, I don’t do that on my calculator because I’m always careful to put it in four and solve for the fifth. So if you’re doing that, you never have to worry about clearing it. But remember, the calculator\n remembers these values even after you turn it off.

So just turning it off and turning it on doesn’t reset any of these values to 0. So, just be aware of that when you’re working problems. And I think it’s best practice to put in these four values. It makes\n you think about it too. Do I have a payment here? Is there a payment at the end I should put in as future value?

So, if you look at the mathematics here, what we’ve got is the present value of some end-of-period payments. If this is the end of the first period, that’s time one, one period from now. And this is time equals\n two. This is N periods from now, supposed to be equal to N there. And then this future value comes on that same date.

So, you get a payment, payment, payment, then you get your last payment, and then anything that’s left in the account or anything that’s left to be paid, that’s the future value at that point in time.

So, we’re discounting these at our interest rate. This is the I/Y that we put into the calculator. This is N, the number of periods. Here’s the payment per period. It could be 0. And here’s the future value\n that could be 0 as well.

Now if they’re both 0, of course, it’s 0. But you could have either payment, you could have a non-zero payment, a non-zero future value, or both, is what I’m trying to say. So, if you put in any four of\n these values in this equation, and you’re in end mode, then you can calculate the 5th. And that’s the essence of what’s going on with these keys.

Now let’s take a look at an example here.

We’ve got a security with a required return of 7%, so we’re adding 7% to one to discount…that makes 6 annual payments beginning 1 year from today, so that’s clearly end mode, and a payment of $1,000\n after 6 years.

Those of you with a little financial training are going to recognize this is like the payments on an annual pay 6% bond, or a semi-annual pay 12% bond. But we’ve got 6 payments here, so let’s think of it as\n a 6-year bond that pays $60 each year, and it matures at $1,000 on the last day, and that’s the same day that the last $60 payment is made.

So, notice that our discount factor is the same for the thousand in the last payment because they come on the same day.

So with your calculator in end mode, just hit 6 and then N, hit seven and I/Y to tell it the discount rate is 7, hit 60 and then payment or enter 60 and then hit the payment key, put in 1,000 and then hit the future value\n key, and compute the present value. And it solves this equation right here.

Notice that it comes back as a negative. The calculator understands, well, it doesn’t really understand, but it’s programmed to act as if it understands that if I put money into an account for a period of time,\n I can take money out at the end.

In this case, if I’ve got a bond that’s going to pay me payments and pay me the face value…that’s why we put those in as positive…then the present value is what I’d have to pay out\n today to buy those. So, that’s why the difference in signs. And if you foul up the difference in signs, then many times you’ll get error message Number 5. And that’s just an indication that that’s\n exactly what you did.

So, as I said, entering any four of these values, present value and future value must usually have different signs or you’ll get this error message Number 5. So, you can think of it as a company issuing a bond.

They take in the present value today and make those coupon payments and maturity payments, so they’d both be negative. Or a buyer of a bond pays out money today, a negative, and then gets the payment and the face\n value at maturity.

Now, sometimes we might want to put the calculator in begin mode. Try to avoid it, but sometimes you do. This is like a lottery payout, right? If you get a lottery payout, you win the lottery. I know most of us haven’t,\n but I still understand how it works if I do.

And if I’m taking an annuity, a series of payments for my lottery winnings, the first one will be the day I show up there with my ticket. They’re not going to say, “Oh, you can have your first payment\n a year from now. Go think about being rich, okay?” No, they’re not that cold-blooded. They give you the first payment when you take your ticket in. So, that’s the beginning-of-the-year payment.

So now, if we have payments that start today, and we have N periods, then here’s our equation. I won’t get too much into mathematics right now, we’re supposed to be talking about how to run your\n calculator.\n

But in this case, put your calculator in begin mode, put in 20 periods, a $200,000 annual payment, a 6% discount rate, and a 0 future value, right? After you get that last…say you got 20 payments for your\n lottery winnings…after you get that last payment, there’s no maturity value. They don’t owe you anything else. So put the future value in as 0, compute the present value, and hopefully, your\n display says negative $2,431,623.298, depending on what rounding you’ve got in there.

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LN and ex Keys on TI BAII Plus

A couple more keys for you that come up not real often but sometimes. Entering a value and then hitting the LN, that’s the natural logarithm, computes the natural log of that value. And how might we use\n this in finance?

Well, if we have an investment, we say its holding period return for 1 year was 5.2%, what is the equivalent continuously compounded rate of return? So, that’s where this log key comes up in Level 1.

So, if we’ve got 5.2% for our holding period return over the whole year, the value of our investment went up 5.2%, we’re going to put in 1.052…and then you see that in the fourth up on the\n left-hand side, hit that LN key, and I get 0.0507.

So, a continuously compounded rate of 5.07% would increase the value of an investment or the value of an asset by 5.2% over the course of a year.

Now, what about that e to the x? Well, that’s the mathematical e, and e to the x says what power do I have to raise e to, to get this number. And that’s really just the opposite of the natural log.\n Because the natural log of e to the x is x, and then if I take e to the x, I get back to that number.

So, now we have the continuously compounded rate of 5.07%, what is the effective annual rate? That is, with a 5.7% rate compounded continuously, by what percentage would a deposit grow over one year?

Well, it’s just the opposite of what we did before. We’re going to put in 0.0507. Now, this is the second function above the log key, hit that e to the X, so 2nd e to the x minus 1, and that\n gets us back to our effective annual rate of return.

So, these only come up in this context that I know of is with continuously compounded rates of return, which are used in continuous-time mathematics foundation to some of our options pricing and things at\n Level 2. So, that’s why it’s in Level 1.

More CFA Calculator Settings

A couple of miscellaneous keys here for you finally. That arrow key that’s right below the on/off, when you punch in a wrong digit, you hit 2nd, hit that arrow key, and…well, you don’t\n have to hit the 2nd. Sorry. It doesn’t matter if you do, but you don’t have to. Just hit that arrow key, and it goes back one digit at a time if you have to correct what you’ve entered\n there.\n

Now, remember, again, even when the calculator is turned off, it remembers the entries in all these cash flow functions, time value of money functions, the memory registers, everything like that.

And one last key that you may find handy is the 2nd function for the equal key. If you hit 2nd and then hit that equal key, it goes back to the last answer you had.

So, if you had an answer and you started to do something to it, divide it by something, or multiply it by something, and you say, “Oh, man, that’s not what I want to do.” If you\n want to get back to that, use the 2nd function, and then hit that equal key.

Okay, well, this is some of the setup and some of the basic things. There are some more calculator functions that we do in another video. It’s called the “Advanced Operation of Your Calculator.” But set it up that way. That way you’ll\n be in agreement with all our examples, the keystrokes we show, answering practice exam problems, and everything like that. So, that’s it for this.

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By: Kaplan Schweser

June 27, 2022

Learn the basic functions of your Texas Instruments (TI) BAII Plus calculator that you will need for the CFAexam. In this article, you will learn how to:

CFA Exam Calculator Basics

In this volume of the Schweser Video Library, we’re going to look at the basic functions and setting up your Texas Instruments Business Analyst II Plus calculator for the CFA exam.

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Video Transcription

So, our examples in the SchweserNotes, although we have some for the HP for specific functions, most of our answers and explanations and examples are based on the Texas Instruments calculator.

Now there’s a plastic one, and then there’s this one called the Professional Edition. So, since I’m a professional, Schweser bought me this one some years back. And it has little rubber feet on it. It’s a little heavier, has a better feel, and the buttons feel cooler when you press them.

In terms of functionality, there are a couple of functions that are on this Professional Edition that aren’t on the other one. Neither of them is very expensive. And as far as I know, they last forever. And never had trouble with one, never replaced the battery. Although I guess, it could happen if you were using it all the time. Mostly, we use Excel these days, so they don’t get used all that much. But you need to be familiar with it for the exam.

CFA Calculator Policy >>

Setting up the TI BAII Plus

So, let’s first talk about setting up your calculator. Now, there are 2nd functions to a lot of these keys, and you’ll see what’s written over the actual key itself. Across the top row, you see it says QUIT, SET, DELETE, INSERT, and all that sort of stuff. And those are the 2nd functions.

Setting the Number of Decimals

So, my accuracy or my precision, I should say, is to 1/100th of a percent. One basis point. And that’s usually, I think, adequate for anything you’re going to face on the exam.

Now the calculator itself is carrying, I forget, seven, eight, nine, digits in its brain, and they’re always there. You’re not changing or rounding anything except what’s in the display. So if you’re using four decimal places, and you get to a problem where for some reason you need the 5th and 6th decimal place, you can just go times 100, it’ll move that over, it’ll move the decimal point, but you’ll see those next two digits just that easily.

So use that 2nd key and find the format key. That’s the 2nd function for the decimal point in the middle of the bottom row. And if I do that, mine reads DEC equals four. If you want something else in there than what you have, then put it in; put four in, for example, and then press ENTER, and then you can clear the display, and that’s how it’s going to display all the time after that.

Setting Payments to the End of the Period

Now, that is right above the PAYMENT key in the third row. So, if I go second and then hit that PAYMENT key, mine says N, so I’m not going to change it. If yours says BEGIN, then press second, and then press that SET button. It’s actually the ENTER button in the upper-left corner there, and that’ll toggle between beginning and end.

When it’s in begin mode, there’s a little BGN that shows up in the upper right-hand corner here and lets you know you’re in begin mode. If it’s in end mode, since that’s the default, there’s no indication of that on the display. So, what you’re essentially telling it, well, there are four payments in this annuity, a little short four-payment annuity.

In end mode, it assumes those payments, deposits into the account, or payments out of the account, are made at the end of each of the next four years or periods. If you put it in begin mode, it assumes that each payment comes at the beginning of those periods. So, the first payment would come today, which is the beginning of the first year or first period.

Setting the Number of Payments Per Period

If it's quarterly, why, we’ll use a quarterly interest rate. N will be the number of quarters. Our payment will be payment per quarter. So, really it says I/Y, but think of it as payments per period, and then we’ll just think in terms of whatever periods we have in the problem we have to deal with. So use the second key and then hit I/Y. The display will read payments per year or payments per period equals, then press one, ENTER, and then you can clear the display again.

Setting Modes of Operation: CHN vs AOS

Now there are two modes of operation. One is CHN, which I assume stands for chain mode, and AOS, which has to do with the order of algebraic operators. Now, take a look at this calculation here.

Now, if we put in 3 plus 5 times 4…so this is what we’re putting in. I’m not putting in any of the parentheses. So, if I just put in 3 plus 5, when I hit times, that also does an equal function in chain mode. So, 3 plus 5 is 8, I hit the times, and then you’ll see 8 in the display, enter 4, enter equal, and you’ll get 32.

Now, if you are set to algebraic operations priorities, then it goes 3 plus 5 times 4. Well, the order of algebraic operations, if I remember, is exponents first, then multiplication and division, and then addition and subtraction. So since this times multiplication operator takes precedence, it multiplies 5 times 4 and then adds 3, so we will get 23.

Now, there are parentheses on this. In the middle there, you can see the left parentheses and the right parentheses, so even if you are set in chain mode, you can insert your own parentheses. So if I did 3 plus…well, if I were in chain mode, and entered this with the parentheses, then I’d get 23. And when you close those parentheses, you have to hit the equal sign after that. Closing the parentheses would give you this value, 20, and then the equal sign would get you to 23.

And you change those with that same format. If I go to the second format, I get my decimal. But I think if I do an up arrow, mine says CHN, which is where I want it. If you want it somewhere else, if you want it in algebraic operator mode, then press 2nd, and press that SET key, the Enter key, and that’ll toggle between Chain and AOS modes.

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The √x, x2, 1/x, and +/– TI BAII Plus Keys

So once we’ve got our calculator set up, now let’s take a look at some of the keys on there. The reason I’ve got these four keys separated out here is that these keys all operate on the number in the display before it does anything with it. And I’ll show you an example of that.

And then, so, those are all right across the fourth row there, and then at the bottom right, we have the plus-minus key, which just changes the sign of whatever is in the display.

Let’s take a look at an example here. And you can see here that these keys operate on the number, and then it moves on. So look at that first example.

If I want 0.89 divided by the square root of 2.17 times 7.3 squared, I just have to enter 0.89, then divide by 2.17. But before it divides, that's the important point here, and it’s really handy. Before it divides, it’ll take the square root of that. And then when I hit the multiplication, it’s multiplying that, the square root…dividing by the square root of 2.17. And then times, I hit 7.3, but I want to square that, so I do that, and then hit equals, and so it multiplies by that, 7.3 squared.

Now, we could do this a different way. Sometimes when there are a lot of things going on in the denominator, it’s easier to punch it in by doing the denominator first. So that’s what I’m illustrating here. I can put in 2.17, take the square root of that, and then hit the 1/X key, and then multiply by 0.89. Well, there's not much difference in work here, but imagine if you had a denominator that was 1.12 to the 7th power. Then it would be easiest to do 1.72 y to the x will take it to the 7th power, then hit the 1/X key, and then multiply by 0.89 or whatever’s in the numerator.

So, that’s just a handy trick. I think one thing you want to try and avoid is writing down any interim results. When you write down an interim result, and then have to put it back in the calculator, there’s always a chance for exam-taking error, dyslexia to take over, or whatever gremlins are in your head at the time. So the less you do that, the less chance there is for making mistakes.

So, I try to do the calculations all kind of in a row within the calculator. If you have to save something, we’ll talk about saving something in the memory function here in just a bit. So, for 2 times minus 3.5, 2 times 3.5, change the sign to minus 3.5 and then equals to get the answer of minus 7. So a little bit of practice and you’ll be very comfortable with these.

TI BAII Plus Exponents yx

Okay, I mentioned taking something to the 7th power. We can’t do that with the x-squared key. With the x squared key, you can get x squared. If you press it twice, you can get X to the 4th. If you press it three times, you can get X to the 8th. But for these other exponents, we’re going to have to use the y to the x key.

So, here’s our example. We want to calculate 1.75 to the 5th power. So, we enter 1.75 and then hit that y to the x key, it’s just above the 9. And so, you hit the y to the x key, hit the 5, and then hit equal, and that’s what it gives you. It gives you 1.75 to the 5th power. So, here’s an example of how we might use that. The example here says, “A firm’s dividends have increased from $2.21 to $3.54 over the last four years.

Calculate the annual compound growth rate of dividends over the period.” Well, first, if we’re going to say, “Well, we’ve got four periods of growth,” then we’re going to use the one-quarter power here. We’re going to take the 4th root.

So, 3.54 divided by 2.21, we want to take that to the 1/4 power. So what we could enter is y to the x, then enter 4, then enter 1/X. Your display will change to 0.25, which is what 1/4 is. And then hit equal, and we need to subtract 1, but we can find out that four periods of compound growth of 12.5% would get us from $2.21 to $3.54.

Now, if it’s pretty obvious what that fractional exponent is, as in this case, we know that 1/4 is 0.25, we could go 3.54 divided by 2.21, hit the y to the x key, put in 0.25, hit equals, subtract 1, and get 12.5% rate of compound growth that way. So, that’s pretty easy with 1/4 or 1/5. Even with 1/3, you can put in 0.3333333, but if it’s 1/7 or something like that, or to the 1/7 power, it’s just as easy to put in 7, hit that 1/X key, and get the decimal equivalent of 1/7.

Storing and Retrieving Results on TI BAII Plus

Now, storing and retrieving results, you’ve got ten memory registers on this, and we’re going to store them using the STO function, the store key, and retrieve them using the recall key. And so every one of those digits on your keypad, 0 through 9, identifies a different storage register.

So, for example, this is a problem derived from the dividend discount model, the constant growth model. And so, what we’re going to do here is do it in pieces. We’re going to take that first piece and go 1 divided by 1.13 equals, and then hit the store, and then 1. And that stores that in register one.

For this third term here, I use the parentheses because remember, I’ve got this in chain mode. And so, I want to take 1.21 and then I want to divide that by 0.13 minus 0.05, 13% minus 5%. And then I want to divide that by 1.13 squared. And when I get that, I can store that in register 3 by hitting the store key, hitting the number 3, and that will store 11.8451.

Just as an aside, you notice that 1.21 divided by 0.13 minus 0.05, another way to do that in chain mode is to go…0.13 minus 0.05, and then hit equals…get 0.08, and then hit that 1/X key, and then multiply that 1.21, and then we can get that answer that way as well. And then we’d have to divide by 1.13 squared.

Now one reason you might want to do problems like that is, say, you’re taking a multiple-choice test, and you get done with a calculation like this, and you look down, and there are no answer choices there that match yours to any significant degree. Well, now, you’ve got to troubleshoot this and find out where the error is.

Well, if you did it all as a single calculation, you just have to start over. If you’ve got the pieces stored in three registers, you can check each piece against what you’ve got stored. When you find one that isn’t right, then store the new value and go plus recall one, plus recall the other one, and then get your answer. And hopefully, by then you’ll find one that’s one of the choices for that problem.

Now, the second memory function shows the value in memory register 0, and then you can use the arrow keys to go through all of those. So that MEM is actually the 0 key, so I’m going to go 2nd function, hit MEM, and it says M0, memory and register 0, and then use the up arrows to go to 9 or the down arrows to take them numerically, M1, M2, M3, M4, right on through.

Now you can clear all these registers by doing 2nd, and then hitting clear work, which is that second function of the lower left-hand key down there. Now I’ve got Y there because I don’t know why you’d ever have to change them. As soon as you put something new into a register, it just overwrites whatever was in there before. So I’ve never had occasion to clear them, but you can if you like.

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TI BAII Plus Combinations

Okay, the next function we want to look at on this calculator is combinations. So, the idea of combinations is in this example.

How many different pairs can be made from the letters A, B, and C?

Well, there should be three different pairs that we can make from that. And so that’s a simple example. It, of course, gets more difficult as, I say, how many pairs are there in 17 or something like that. But this nCr function, which is above the 2nd function above the plus key on the right-hand side there, that answers this question…uses the formula.

This is one place in which the Texas Instruments calculator has a function that the HP does not.

So, we just go three, and then hit that second function and then the plus key to get that nCr, and then put in two. So you’ve really asked the calculator, “How many groups of two can I pull from an overall group of size three?” and that will display three, and those are our three pairs.

Now, notice we don’t count AB and BA separately when we’re using the nCr, the combination function is there. So, let’s look at a different question. How many different pairs are there in four items? Well, if we enter four, take that nCr function, two equals, that gives us the answer of six.

Permutations

Now, when order does actually matter, then we’re talking about permutations. So, now we’re going to count AB and BA as two different pairs when we talk about permutations.

So, all we have to do is, it functions exactly the same, enter three, take that 2nd function, nPr, and then two, and then equal to display six.

So, let’s take a look at an example of how that might come up. Well, this isn’t exactly a finance application but should help anyway.

If there are seven runners in a race, how many different ways can runners finish 1st, 2nd, and 3rd?

So now order matters, right? Three runners in this order in 1st, 2nd, and 3rd is a different outcome from those same three runners in a different order in 1st, 2nd, and 3rd place.

So the question here, how many groups could win the first three places in any order? And seven 2nd nCr, the combination formula, gives us an answer of 35.

Time Value of Money Keys on TI BAII Plus

If you put in any of those four values, and then you press on the fifth one and press compute, it’ll calculate it for you based on those values you put in for the other four.

Now, sometimes, as a shortcut, people hit this clear time value of money, and that’s out there above the FV, future value key, it’s the second function of that.

Now, I don’t do that on my calculator because I’m always careful to put it in four and solve for the fifth. So if you’re doing that, you never have to worry about clearing it. But remember, the calculator remembers these values even after you turn it off.

So just turning it off and turning it on doesn’t reset any of these values to 0. So, just be aware of that when you’re working problems. And I think it’s best practice to put in these four values. It makes you think about it too. Do I have a payment here? Is there a payment at the end I should put in as future value?

So, if you look at the mathematics here, what we’ve got is the present value of some end-of-period payments. If this is the end of the first period, that’s time one, one period from now. And this is time equals two. This is N periods from now, supposed to be equal to N there. And then this future value comes on that same date.

Now if they’re both 0, of course, it’s 0. But you could have either payment, you could have a non-zero payment, a non-zero future value, or both, is what I’m trying to say. So, if you put in any four of these values in this equation, and you’re in end mode, then you can calculate the 5th. And that’s the essence of what’s going on with these keys.

Now let’s take a look at an example here.

Those of you with a little financial training are going to recognize this is like the payments on an annual pay 6% bond, or a semi-annual pay 12% bond. But we’ve got 6 payments here, so let’s think of it as a 6-year bond that pays $60 each year, and it matures at $1,000 on the last day, and that’s the same day that the last $60 payment is made.

So, notice that our discount factor is the same for the thousand in the last payment because they come on the same day.

So with your calculator in end mode, just hit 6 and then N, hit seven and I/Y to tell it the discount rate is 7, hit 60 and then payment or enter 60 and then hit the payment key, put in 1,000 and then hit the future value key, and compute the present value. And it solves this equation right here.

In this case, if I’ve got a bond that’s going to pay me payments and pay me the face value…that’s why we put those in as positive…then the present value is what I’d have to pay out today to buy those. So, that’s why the difference in signs. And if you foul up the difference in signs, then many times you’ll get error message Number 5. And that’s just an indication that that’s exactly what you did.

And if I’m taking an annuity, a series of payments for my lottery winnings, the first one will be the day I show up there with my ticket. They’re not going to say, “Oh, you can have your first payment a year from now. Go think about being rich, okay?” No, they’re not that cold-blooded. They give you the first payment when you take your ticket in. So, that’s the beginning-of-the-year payment.

But in this case, put your calculator in begin mode, put in 20 periods, a $200,000 annual payment, a 6% discount rate, and a 0 future value, right? After you get that last…say you got 20 payments for your lottery winnings…after you get that last payment, there’s no maturity value. They don’t owe you anything else. So put the future value in as 0, compute the present value, and hopefully, your display says negative $2,431,623.298, depending on what rounding you’ve got in there.

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LN and ex Keys on TI BAII Plus

So, if we’ve got 5.2% for our holding period return over the whole year, the value of our investment went up 5.2%, we’re going to put in 1.052…and then you see that in the fourth up on the left-hand side, hit that LN key, and I get 0.0507.

So, a continuously compounded rate of 5.07% would increase the value of an investment or the value of an asset by 5.2% over the course of a year.

Now, what about that e to the x? Well, that’s the mathematical e, and e to the x says what power do I have to raise e to, to get this number. And that’s really just the opposite of the natural log. Because the natural log of e to the x is x, and then if I take e to the x, I get back to that number.

So, now we have the continuously compounded rate of 5.07%, what is the effective annual rate? That is, with a 5.7% rate compounded continuously, by what percentage would a deposit grow over one year?

Well, it’s just the opposite of what we did before. We’re going to put in 0.0507. Now, this is the second function above the log key, hit that e to the X, so 2nd e to the x minus 1, and that gets us back to our effective annual rate of return.

More CFA Calculator Settings

A couple of miscellaneous keys here for you finally. That arrow key that’s right below the on/off, when you punch in a wrong digit, you hit 2nd, hit that arrow key, and…well, you don’t have to hit the 2nd. Sorry. It doesn’t matter if you do, but you don’t have to. Just hit that arrow key, and it goes back one digit at a time if you have to correct what you’ve entered there.

Now, remember, again, even when the calculator is turned off, it remembers the entries in all these cash flow functions, time value of money functions, the memory registers, everything like that.

And one last key that you may find handy is the 2nd function for the equal key. If you hit 2nd and then hit that equal key, it goes back to the last answer you had.

So, if you had an answer and you started to do something to it, divide it by something, or multiply it by something, and you say, “Oh, man, that’s not what I want to do.” If you want to get back to that, use the 2nd function, and then hit that equal key.

Okay, well, this is some of the setup and some of the basic things. There are some more calculator functions that we do in another video. It’s called the “Advanced Operation of Your Calculator.” But set it up that way. That way you’ll be in agreement with all our examples, the keystrokes we show, answering practice exam problems, and everything like that. So, that’s it for this.

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