## HP 20b

#### Definitions & Other

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The Hewlett Packard 20b Business Consultant is a very easy to use financial calculator that will serve you well in all finance courses. This tutorial will demonstrate how to use the financial functions to handle time value of money problems and make financial math easy. I will keep the examples rather elementary, but understanding the basics is all that is necessary to learn the calculator.

Please note that in the following text the blue key (above the ON/CE key) is referred to as Shift because it is used to shift to the blue-colored function below the key that is pressed next.

## Initial Setup

Before we get started, we need to correctly (in my view, anyway) set up the calculator. The 20b comes from the factory set to assume monthly compounding. That's fine, I suppose, but its better to set it to assume annual compounding and then make manual adjustments when you enter numbers. Why? Well, the compounding assumption is hidden from view and in my experience people tend to forget to set it to the correct assumption. Of course, most people don't recognize a wrong answer when they get one, so they blithely forge ahead. To fix this problem press 1 (once per year) then Shift and finally PMT. To check that it has taken, press RCL (recall) and then Shift PMT. You should see P/YR = 1 on the screen. Problem solved. Now, just make sure that you always enter the total number of periods (not necessarily years) into N, the per period interest rate into I/YR, and the per period payment into PMT.

Many old-timers (like me!) and engineering-types prefer calculators that use RPN data entry, while most people prefer to use algebraic data entry. The HP 20b Business Consultant will accomodate either preference. If you don't know which you prefer, you are almost certainly used to using an algebaric calculator and you don't need to change anything. On the other hand, if you prefer RPN then you can set the 20b to use that method by pressing Shift ( (Mode). Now, press the down arrow button 5 times until you see Chain (or RPN or Algebraic) on the screen. Next, press INPUT until RPN appears. To exit from the Mode settings, press ON/CE. Note that when the calculator is in RPN mode, you will see an RPN indicator (HP calls it an "annunciator") on the far right side of the screen. I will not explain RPN data entry here. Instead, I'll just say that it is a more efficient way to enter calculations and it is worth learning.

One other adjustment is important. By default the 20b displays only two decimal places. This is not enough. Personally, I like to see five decimal places, but you may prefer some other number. To change the display, press Shift ( (Mode), and finally the numeric key that corresponds to the number of digits you would like to see displayed. I would press Shift ( 5 to display 5 decimal places. To exit from the Mode settings, press ON/CE.That's it, the calculator is ready to go.

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## Example 1 - Future Value of Lump Sums

We'll begin with a very simple problem that will provide you with most of the skills to perform financial math on the 20b:

Suppose that you have $100 to invest for a period of 5 years at an interest rate of 10% per year. How much will you have accumulated at the end of this time period? In this problem, the$100 is the present value (PV), N is 5, and I/YR is 10%. Before entering the data you need to make sure that the financial registers (each key is nothing more than a memory register) are clear. Otherwise, you may find that numbers left over from previous problems will interfere with the solution to this one. Press RCL PV (or any other TVM key) and then Shift RESET to clear the memory. (Be careful here: this will also change the P/YR setting back to 12. The alternative is to remember to enter 0 into any TVM key that you aren't using for the problem - this is what I recommend.) Now all we need to do is enter the numbers into the appropriate keys: 5 into N, 10 into I/YR, -100 into PV, and 0 into PMT. Now to find the future value simply press FV. The answer you get should be 161.05.

If you didn't get the correct answer, then you likely need to check to be sure that you have the P/YR set to 1. If it is set to 12, you would get an incorrect answer of 104.23 because the calculator thinks that you invested for only 5 months. Again, the P/YR setting is one to keep an eye on.

### A Couple of Notes

1. Every time value of money problem has either 4 or 5 variables. Of these, you will always be given 3 or 4 and asked to solve for the other. In this case, we have a 4-variable problem and were given 3 of them (N, I/YR, and PV) and had to solve for the 4th (FV). To solve these problems you simply enter the variables that you know in the appropriate keys and then press the other key to get the answer.
2. The order in which the numbers are entered does not matter.
3. When we entered the interest rate, we input 10 rather than 0.10. This is because the calculator automatically divides any number entered into I/YR by 100. Had you entered 0.10, the future value would have come out to 100.501 — obviously incorrect.

In this case, we already know the future value ($100,000), the number of periods (18 years), and the per period interest rate (8% per year). We want to find the present value. Enter the data as follows: 18 into N, 8 into I/YR, and 100,000 into FV. Note that we enter the$100,000 as a positive number because you will be withdrawing that amount in 18 years (it will be a cash inflow). Now press PV and you will see that you need to invest $25,024.90 today in order to meet your goal. That is a lot of money to invest all at once, but we'll see on the next page that you can lessen the pain by investing smaller amounts each year. ## Example 1.2 — Solving for the Number of Periods Sometimes you know how much money you have now, and how much you need to have at an undetermined future time period. If you know the interest rate, then we can solve for the amount of time that it will take for the present value to grow to the future value by solving for N. Suppose that you have$1,250 today and you would like to know how long it will take you double your money to $2,500. Assume that you can earn 9% per year on your investment. This is the classic type of problem that we can quickly approximate using the Rule of 72. However, we can easily find the exact answer using the HP 20b calculator. Enter 9 into I/YR, -1250 into PV, and 2500 into FV. Now solve for N and you will see that it will take 8.04 years for your money to double. One important thing to note is that you absolutely must enter your numbers according to the cash flow sign convention. If you don't make either the PV or FV a negative number (and the other one positive), then you will get ER: No Solution on the screen instead of the answer. That is because, if both numbers are positive, the calculator thinks that you are getting a benefit without making any investment. If you get this error, just press ON/CE to clear it and then fix the problem by changing the sign of either PV or FV. ## Example 1.3 — Solving for the Interest Rate Solving for the interest rate is quite common. Maybe you have recently sold an investment and would like to know what your compound average annual rate of return was. Or, perhaps you are thinking of making an investment and you would like to know what rate of return you need to earn to reach a certain future value. Let's return to our college savings problem from above, but we'll change it slightly. Suppose that you are planning to send your daughter to college in 18 years. Furthermore, assume that you have determined that you will need$100,000 at that time in order to pay for tuition, room and board, party supplies, etc. If you have $20,000 to invest today, what compound average annual rate of return do you need to earn in order to reach your goal? As before, we need to be careful when entering the PV and FV into the calculator. In this case, you are going to invest$20,000 today (a cash outflow) and receive $100,000 in 18 years (a cash inflow). Therefore, we will enter -20,000 into PV, and 100,000 into FV. Type 18 into N, and then press I/YR to find that you need to earn an average of 9.35% per year. Again, if you get ER: No Solution instead of an answer, it is because you didn't follow the cash flow sign convention. Note that in our original problem we assumed that you would earn 8% per year, and found that you would need to invest about$25,000 to achieve your goal. In this case, though, we assumed that you started with only \$20,000. Therefore, in order to reach the same goal, you would need to earn a higher interest rate.

When you have solved a problem, always be sure to give the answer a second look and be sure that it seems likely to be correct. This requires that you understand the calculations that the calculator is doing and the relationships between the variables. If you don't, you will quickly learn that if you enter wrong numbers you will get wrong answers. Remember, the calculator only knows what you tell it, it doesn't know what you really meant.

Please continue on to part II of this tutorial to learn about using the HP 20b to solve problems involving annuities and perpetuities.