You can use the TI-83 Plus graphing calculator to determine the best interest rate. When nominal rates (also called annual percentage rates) are compounded at different frequencies (as are those following), you can compare them to each other only by converting them to effective rates (the simple-interest equivalent of nominal rates).

Which of the following is the best interest rate for a savings account?

• 5.120% annual rate, compounded monthly

• 5.116% annual rate, compounded daily

• 5.115% annual rate, compounded continuously

## How to find the effective rate on the TI-83 Plus

To find the effective rate given the nominal rate:

1. Set the second line of the Mode menu to Float.

When dealing with money, you usually set the second line of the Mode menu to 2 so all numbers are rounded to two decimal places. When you’re comparing interest rates, however, you want to see as many decimal places as possible. You can do so by setting the second line to Float.

2. Press [APPS][1] to start the Finance application. (On the TI-83, press [2nd][x–1].)

3. Repeatedly press

to move the indicator to the Eff command and press [ENTER].

4. Enter the nominal rate, press [.], enter the number of compounding periods per year, and press [ ) ][ENTER].

When interest is compounded continuously, it is compounded an infinite number of times a year. But there is no way of entering infinity into the calculator. You can get around this problem by entering a very large number, such as 1012, for the number of compounding periods. The fastest way to enter this number is to press [2nd][.] and then enter the number 12.

The answer to the question posed at the beginning of this section is 5.116%, compounded daily (the choice that gives you the largest effective rate).

You can easily use the same command over and over, if (after using the command the first time) you press [2nd][ENTER] to recopy the command to the next line on the screen. Then edit the entries in the command and press [ENTER] to execute the command.

## How to find the nominal rate on the TI-83 Plus

The steps that convert an effective rate to a nominal rate are similar to those already listed. To begin, you follow the first two of those steps — and then (in Step 3), select the Nom command instead of the Eff command. In Step 4, you enter the effective rate (after the comma, enter the number of compounding periods for the nominal rate).