Why Rounded Calculator Displays Change Effective Annual Rate Results

Summary

The document describes a Texas Instruments BA II Plus calculation of an effective annual rate from a nominal rate compounded daily. The user rounds the intermediate value shown on the calculator to five decimal places, then raises that displayed value to the number of compounding periods. This produces a different result from evaluating the full expression at full internal precision.

The reply explains that entering the entire expression lets the calculator retain additional decimal places in the intermediate calculation, yielding a different annualized result. The example illustrates how rounding before exponentiation can magnify small errors. It is a narrow calculator-use example, not a general guide to the calculator’s settings or to effective-rate conventions; the stated result depends on the inputs and precision used.

Key ideas

• Rounding an intermediate value before exponentiation can materially alter the final result.
• The calculator may retain more precision internally than it displays.
• Entering the full expression avoids using the rounded display value as a new input.
• The example concerns effective annual rate arithmetic and does not address other compounding conventions.

Tags

# When using exponents the BA II Plus is returning incorrect answers, what am I doing wrong?


# When using exponents the BA II Plus is returning incorrect answers, what am I doing wrong?












I am using the BA II Plus Texas Instruments calculator.

When I want to calculate an EAR for example, my calculation would be as follows:

(1 + r/m )^m -1 = EAR

So in my calculator, using 5 decimal places I press:

```
1 + ( .03 / 365 ) =
```

This give me the answer:

```
1.00008
```

Then without pressing anything else, I press:

```
y^x 365
```

Which gives me the answer of:

```
1.03045
```

This is the wrong answer since the correct answer to 1.00008^365 is actually 1.02963

Is there something wrong with my calculator? The operations seem to be exactly the same...

## Answer by John Sonnino (score 1)

https://quant.stackexchange.com/a/71300

The answer as it turns out is quite straight forward.

When using the complete equation, the calculator works out the answer with the full number of decimal places i.e. 1.00008219^365 = 1.03045259

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.