**Lump Sum Calculations**

The TI 84 Plus is an easy to use financial calculator which 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.

**Initial Setup**

There is one adjustment which needs to be made before using this calculator. By default, the TI 84 Plus 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 `MODE`, then the `⯆` (down arrow) key once (to the Float line). Next, use the `⯈` (right arrow) key to highlight the 5 and press Enter. Finally, press `2nd` `MODE` to exit the menu. That’s it, the calculator is ready to go.

This tutorial will make extensive use of the TVM Solver, but the TI 84 Plus offers additional financial functions in the Finance menu.

If you have come here because you are experiencing a problem, you might check out the FAQ. If you don’t find the solution, please send me a note.

**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 TI 84 Plus:

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 put the calculator into the TVM Solver mode. Press the `APPS` button, choose the Finance menu, and then choose TVM Solver . Your screen should now look like the table below:

Field | Entry |
---|---|

N | 5 |

I% | 10 |

PV | -100 |

PMT | 0 |

FV | 0 |

P/Y | 1 |

C/Y | 1 |

Enter the data as shown in the table making sure that PMT is set to `0`. Now to find the future value simply scroll down to the FV line and press `ALPHA` `ENTER`. 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 on the appropriate lines and then scroll to the line for the variable you wish to solve for. To get the answer press
`ALPHA``ENTER`. Be sure that any variables not in the problem are set to 0, otherwise they will be included in the calculation. - The order in which the numbers are entered does not matter.
- Always make sure that the P/Y (payments per year) and C/Y (coupons per year) are set to 1. At least this is what I prefer. Since these are visible on the screen at all times, it is not strictly necessary. If you can remember to change these to the appropriate values for each problem (1 for annual compounding, 12 for monthly compounding, etc) then you’ll have no problems.
- When we entered the interest rate, we input 10 rather than 0.10. This is because the calculator automatically divides any number entered on the I% line by 100. Had you entered 0.10, the future value would have come out to 100.501, which is obviously incorrect.
- Notice that we entered the 100 in PV 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
`(–)`. - 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 then 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. Go to the TVM Solver and 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 move to PV and press `ALPHA` `ENTER` 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 to 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 TI 84 Plus calculator. Enter `9` into I%, `-1250` into PV, and `2500` into FV. Now scroll up to N and press `ALPHA` `ENTER` 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 ERR: DOMAIN 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 `2` (Goto) to return to the TVM Solver 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 solve for I% to find that you need to earn an average of 9.35% per year. If you get ERR: NO SIGN CHNG instead of an answer, it is because you didn’t follow the cash flow sign convention. Press 2 to return to the TVM Solver and fix the problem.

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 TI 84 Plus to solve problems involving annuities and perpetuities.

Next: TI 84 Plus Page 2