## HP 12C Tutorial

Part I

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The HP 12C is a fairly easy to use financial calculator that will serve you well in all finance courses. Actually, its very easy if you already know RPN (reverse polish notation — a much better way to enter data into a calculator than the algebraic method that you are probably familiar with). 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. I will make no effort here to teach RPN as it isn't necessary for our purposes.

**Please note that there are two versions of the HP 12C**: The original one (in the picture), and the newer 12C Platinum. They are almost identical, but the 12C Platinum is faster and allows you to use algebraic data entry like most other calculators. I still recommend that you use the RPN mode. It takes some time to get used to initially, but it is worth it in the long run.

## Initial Setup

One adjustment is important before we get started. By default the 12C 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 f and then the number of decimal places you wish to display. I would press f 5 to display 5 decimal places. That's it, the calculator is ready to go.

If you have questions about the 12C, please check the FAQ. If the answer isn't there, drop me a note and maybe I'll know the answer.

## 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 12C:

*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 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 cleared. Otherwise, you may find that numbers left over from previous problems will interfere with the solution to this one. Press f X><Y (just to the left of CLX) to clear the financial key memory. Now all we need to do is enter the numbers into the appropriate keys: 5 into N, 10 into i, -100 into PV. Now to find the future value simply press the FV key. The answer you get should be 161.05.

### A Couple of Notes

- Every time value of money problem has either 4 or 5 variables (corresponding to the 5 basic financial keys). 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, 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.
- The order in which the numbers are entered does not matter.
- 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 by 100. Had you entered 0.10, the future value would have come out to 100.501 — obviously incorrect.
- Notice that we entered the 100 in the PV key as a negative number. This was on purpose. Most financial calculators (and spreadsheets) follow the
*Cash Flow Sign Convention*. This is simply a way of keeping the direction of the cash flow straight. Cash inflows are entered as positive numbers and cash outflows are entered as negative numbers. In this problem, the $100 was an investment (i.e., a cash outflow) and the future value of $161.05 would be a cash inflow in five years. Had you entered the $100 as a positive number no harm would have been done, but the answer would have been returned as a negative number. This would be correct had you borrowed $100 today (cash inflow) and agreed to repay $161.05 (cash outflow) in five years. Do not change the sign of a number using - (the "minus" key). Instead, use CHS (change sign). - We can change any of the variables in this problem without needing to re-enter all of the data. For example, suppose that we wanted to find out the future value if we left the money invested for 10 years instead of 5. Simply enter 10 into N and solve for FV. You'll find that the answer is 259.37.

## Example 1.1 — Present Value of Lump Sums

Solving for the present value of a lump sum is nearly identical to solving for the future value. One important thing to remember is that the present value will always (unless the interest rate is negative) be less than the future value. Keep that in mind because it can help you to spot incorrect answers due to a wrong input. Let's try a new problem:

*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 believe that you can earn an average annual rate of return of 8% per year, how much money would you need to invest today as a lump sum to achieve your goal?*

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, 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.

**Important Note: **The HP 12C always gives an integer answer when solving for N. This means that it is often "incorrect." Actually, it is better to say that it is less "exact" than other calculators, but more correct. Let me explain what I believe the original logic was when the engineers made this decision. Most of the time when you are solving for N, you want to know how many payments it will take to retire a loan. If the "exact" answer is, say, 25.08 then that means 25 full payments plus a partial payment. I think that the original logic was that a partial payment is still a payment, just not for the same amount as the others. Therefore, instead of reporting 25.08 as the answer, the 12C will report 26. The non-integer answer that you get from other calculators isn't really exact either because of the compounding assumptions made on that last partial payment. If you need to calculate the number of payments in that way, I suggest that you use a spreadsheet or refer to the appropriate formula. On to our example:

*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 (not quite exact) answer using the HP 12C calculator. Enter 9 into i, -1250 into PV, and 2500 into FV. Now solve for N and you will see that it will take 9 years for your money to double. Now, as mentioned above, this is not exact. The exact answer is 8.04 years.

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 Error 5 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 CLx 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 to find that you need to earn an average of 9.35% per year. Again, if you get Error 5 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 12C to solve problems involving annuities and perpetuities.