James Madison University

**O U T L I N E**

## The basics

Most calculator are designed so that many keys serve double-duty or triple-duty to keep hand-held calculators small, but useful, for many different types of calculations. For example, in the HP10B calculator the key labeled y^{x}is used for both multiplication ("x") and raising a value to a power ("y^{x}"). How do you raise some value to a power? You first strike the orange-colored key, n, and then y^{x}). The orange-colored key tells the computer to use the second function (y^{x}) of this key.Examples (using the HP10B): - Multiplying one value by another (for example, 3 x 4):
3 x 4 = with the answer, 12, displayed.

- Raising a value to a power (for example,
3
^{4}),3 n y

^{x}4 n y^{x}with an answer of 81. You'll notice that you had to strike the n and y

^{x}keys twice in this calculation, but we did not have to use the = key.

Access to the double or triple level functions differs among calculators. For the HP10B, the alternate function of a key is accessed by using the orange-colored key, n. In other models the alternative function may be accessed through, for example, a 2nd key or a g key. You need to refer to the manual that came with your financial calculator to see how to access these second or third level functions.

In addition to access to different levels through a single key, some calculators, such as the HP17B and HP19B, have a set of unidentified keys (just below the display) that perform a function assigned to them based on the "screen" shown in the display. For example, if you select the time value of money screen (by striking the n key below the "FIN" in the display and then the n below the "TVM" in the display), these keys are assigned to represent "PV" , "N", "FV", and so on.

In the examples that follow, the keys are described by the label corresponding to the function you are using. For example, to calculate 3

^{4}on the HP10B, the key strokes are indicated as:3 n y

^{x}4 n y^{x}putting the key's label in the box representing the key to indicate which key to hit. In the case of keys identified by a display screen, such as for the HP19B, we indicate the keystroke in a like manner.

The basic math calculations (such as addition, subtraction, multiplication, and division) are similar among the different brands and models. With the exception of the HP12C, the math is performed much like you would if you were doing it without the calculator. Consider the problem of multiplying 3 by 4:

All models except HP12C: 3 x 4 =

Division, addition, and subtraction are performed in a like manner.The HP12C uses reverse-Polish notation, which is tough to get used to but becomes a time-saver in complex calculations.

HP12C: 3 ENTER 4 x

Let's look closely at an example using the HP10B calculator to solve a future value problem: If an investor deposits $1,000 today in an account that pays 5% interest each year, how much will be in the account at the end of 10 years? The following are given in the problem description:

Present value (PV) = $1,000

and we want to solve for FV. The first thing we need to do is tell the computer the present value. However, in the HP10B (like most financial calculators), we have to change the sign on the present value in order for the calculator's program to work. We input $1,000 as the present value and change its sign,

Interest rate per period (r) = 5% per year

Number of periods (t) = 10 years

1 0 0 0 +/- PV

We then need to tell the computer the interest rate, in whole numbers (that is, 5% is "5"):

5 I/YR

The number of compounding periods is next,1 0 N

And we solve for the future value by striking the FV key, FV. The future value, $1,628.90, will then be displayed.

- Multiplying one value by another (for example, 3 x 4):
## Tips

Your calculator may come from the factory with certain display and calculation settings. For example, the HP10B comes ready to perform calculations using 2 decimal places (a display setting) and twelve payments per year (a calculation setting). If you need more precision, you need to adjust the display. Also, if you require one payment per period, as in most of our calculations, you need to adjust the payments per year.*Get your calculator ready to use.*Use at least four places to the right of the decimal place for all calculations. When working with interest rates, it is very important to use more than two decimal places. You can set your calculator's display program to display a specified number of decimal places. To change the setting to display four decimal places, for example:*Adjust the number of digits displayed.*HP10B n DISP 4

HP12C f 4

HP17B DSP FIX 4 INPUTMost calculations require one interest compounding per period. Since this is the case, we need to make sure that the calculator program we are using considers only one compounding per period.**Check the frequency of payments.**HP10B 1 nP/YR

HP12C frequency of payments within a period is not programmed

HP17B FIN TVM OTHER P/YR 1 INPUTMany calculators allow you to key in a value and then key in how many times that value is repeated. For example, if you have to input six consecutive cash flows of $1 each in your HP12C,**Use short-cuts whenever possible.**

1 g CF

where the sequence " 6 g N_{j}6 g N_{j}_{j}" tells the calculator's program that the one dollar cash flow is repeated six times. In the case of the HP17B and the HP19B, the shortcut for cash flows is the prompt "#TIMES" that corresponds to a period's cash flow.The information you input and the results of the calculations you perform are stored in the computer's registers (its memory for the bits and pieces of information). Clear your registers before starting a new calculation. If you fail to clear the registers in your calculator, you will find that the next problem you do will use data left over from the last problem -- even if you had turned off your calculator since the last problem. To clear your calculator:**Clear the calculator's registers after each problem.**HP10B Clear All

HP12C f REG

HP17B CLEAR DATA

In the case of the HP17B, which allows storage of individual cash flow data, you need to clear the cash flow information separately: n CLEAR DATA YES

Check to see whether your calculator is programmed to assume cash flows at the end of the period or the beginning of the period. Many calculator brands allow you to specify when cash flows occur (beginning or end of the period), which is useful for annuity due calculations. However, like most registers in the calculator, the calculator remembers the last way you specified the cash flows, so you must change this register if you, say, switch from an annuity due to an ordinary annuity calculation.**Check the timing of the cash flows.**To change the setting from end-of-period to beginning-of-period,

HP10B n BEG/END

HP12C g BEG

HP17B FIN TVM OTHER BEG EXITAlways check for the reasonableness of your calculations; it's very easy to hit the wrong key -- especially when taking tests. Learn to do your problem with your calculator and then either check your answers using another method, such as algebra or with the tables of factors, or simply use common sense checks for reasonableness.**Check your work.**

## Examples