Most students have had access to powerful calculators since their high-school years. Unfortunately, many have never learned to use them. In the finance section of this course, you will be shown the best way to perform the calculations using a calculator. The purpose of this web-page is to present some of the basic principles regarding the use of calculators.
The basic mathematical operations are negation, exponentiation, multiplication, division, addition, and subtraction. All but negation are done the same way on most of the calculators that you are likely to encounter though the operator (the symbol used to indicate the corresponding operation) may differ from one calculator to another. For negation, there two commonly used operators and those operators are used in different ways as illustrated in the examples.
| Operation | Operator | Example |
| Negation |
or
 |
the negation of 4 is
4 or 4
|
| Exponentiation |
or
or
 |
4 to the third power is 4
3 or 4
3 or 4
3 |
| Multiplication |
or
 |
4 times 3 is 4
3
or 4
3 |
| Division |
 or
 |
4 divided by 3 is 4
3
or 4
3 |
| Addition |
 |
4 plus 3 is 4
3 |
| Subtraction |
 |
4 minus 3 is 4
3 |
Some operations have a higher precedence (or higher priority) than others. Operations with higher precedence are done before operations with lower precedence. In the list below, the operations are shown in order of decreasing precedence (with the highest precedence at the top). Operations with equal precedence are evaluated from left to right.
Parentheses are used to override the normal order in which operations are performed. Expressions enclosed within parentheses have a higher precedence than even negation. Here are some examples:
| Example | Expression | Interpretation | Evaluation | Value |
| 1 | 2 + 3 × 4 | 2 plus the product of 3 and 4 |
2
3
4 |
14 |
| 2 | (2 + 3) × 4 | the sum of 2 and 3 times 4 |
2
3
4 |
20 |
| 3 | 4 * 32 | 4 times the square of 3 | 4
3
2 |
36 |
| 4 | (4 + 3)2 | the square of the sum of 4 and 3 |
4
3
2 |
49 |
| 5 |
 |
12 divided by the sum of 2 and 4 | 12
2
4
|
2 |
| 6 |
 |
4 plus the quotient of 12 and 2 | 12
2
4 |
10 |
| 7 |
 |
7 minus 4 is divided by 5 |
7
4
5 |
0.6 |
| 8 |
 |
7 minus the quotient of 4 and 5 |
7
4
5 |
6.2 |
Notice that in the 5th and 7th examples, parentheses were needed in the calculator solution even though no parentheses were used in the original expression. That is because the original expressions were written in a vertical format in which the horizontal line indicates both division and that the addition (or subtraction) operation is to be done first. When the same expressions are written in a horizontal format, the division operation is indicated by the normal division operator and parentheses must be used to indicate that the addition (or subtraction) must be done first.
You may have noticed that I didn't mention the precedence of the negation operation in the preceding section. That is because there is no universal consensus regarding negation. Most of the time, negation follows exponentiation in the precedence table. However, in Microsoft Excel, negation has a higher precedence than exponentiation:
| Expression | Interpretation | Evaluation | Value |
| -32 | TI-83: the negation of the square of 3 |
3
2 |
-9 |
| -32 | Excel: the square of negative 3 | - 3 ^ 2 | 9 |
Fortunately for us, none of our problems involve this particular kind of operation. However, I thought you ought to be aware of this difference between calculators and Microsoft Excel.
The best advice I can give you here is to never write down intermediate results and use them to complete a calculation. Learn how to enter the entire calculation all at once into the calculator. There are two specific reasons for this advice:
Let me illustrate how using intermediate results leads to errors. To find the future value of 100 invested at 5% compounded monthly for 10 years, I need to evaluate the following mathematical expression:
The correct way to perform this calculation is to enter it all at once, just as it is written:
100
1
0.05
12
120
which yields $164.70
You may be tempted to perform the calculations one at a time writing down the intermediate results:
0.05 12
is about .0042
1 .0042
is 1.0042
1.0042
120 is about 1.6536
Finally, 100
1.6536 is
$165.36
Notice that the final result is 66 cents larger than it should be. The error can be reduced if you do not round an intermediate result but rather use the value as it is displayed on the calculator. For example, 0.05 divided by 12 is 0.0041666667 rather than 0.0042. Even so, using intermediate results is actually more work than just entering the expression all at once as illustrated above.
The second problem with this piecemeal approach is that it cannot be used at all in Excel. In Excel you will have to enter the expression all at once. Why not just learn to enter it all at once on the calculator as well?
Many people have never learned the difference between truncating and rounding. Consider even a simple calculation such as 0.05/12. The result on a TI-83 calculator is .0041666667. If asked to round this to four decimal places, the majority of students would say it was 0.0041 which is incorrect. The value .0041 is what you get when you truncate .0041666667 to four decimal places. Truncation means you just remove (cut off) everything after the fourth decimal place leaving .0041.
Rounding involves one more step. You need to look at the first digit in the part you removed. If that digit is five or greater then you need to add one to the right-most digit of your truncated result. In our example, the truncated result was .0041 and the part that was removed was 666667. Since the first digit of the removed part is greater than or equal to five, you need to add one to the last digit in the truncated result which yields .0042. This is a more accurate result because .0041666667 is closer to .0042 than it is to .0041.
Let's round 7/12 to four decimal places. On a TI-83 calculator, 7/12 is .0058333333. When I truncate this to four decimal places, I remove the last six digits 333333 leaving .0058. Since the first digit of the part that I removed is less than five, I am done.