Formulas STEM 11. Two mathematical formulas that students at this level of mathematics are familiar with are:

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Arabella Malone
8 years ago
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1 Formulas STEM 11 One definition of the word formula is a conventionalized statement expressing some fundamental principle. Adding the word mathematical to formula we can define a mathematical formula as a conventionalized equation using a group of symbols to express a fundamental numerical principle. Two mathematical formulas that students at this level of mathematics are familiar with are: The Pythagorean Theorem:, which discusses the length of sides of a right triangle. The Quadratic Formula: which we recently used to find x-intercepts of quadratic equations. These formulas are very important in mathematics and will be used repeatedly if one continues further in mathematics. However, from the perspective of a business major, these formulas have a much more limited value. The unfortunate situation that occurs here is that too often only the actual value of the formula is considered and not the thought process skills that are developed from learning these formulas. As one goes through today s activity, the ability to work with formulas will shine. At this point in time, we will begin with a study of the compound interest formula. This equation is very useful in understanding personal finance and appears often in math courses. Thus, it is important that all students have some experience with this equation. From a standpoint of developing skills for STEM majors, it is another opportunity to work with a multitude of different letters. ( ) Where: Consider that you have $10,000 to deposit in a bank and plan to leave it in the bank for 10 years. You bank choices are: Bank A is offering an interest rate of 7.02% and is compounding your money every six months. Bank B is offering an interest rate of 6.96% and is compounding your money every quarter. Bank C is offering an interest rate of 6.89% and is compounding your money every month.

Two mathematical formulas that students at this level of mathematics are familiar with are: The Pythagorean Theorem:, which discusses the length of sides of a right triangle.

2 Quickly, choose one bank and explain why it is the bank you desire to place your money in. Next, use the simple interest formula to compute the exact amount that would be in each bank at the end of ten years. (Note: we will explain below that the amount should be approximately $20,000. If you answers are not close to $20,000 please reconsider how you are computing the answer.) Bank A = Bank B = Bank C = How do the results compare to your initial guess? Formulas in mathematics are much simpler to learn as they are consistent throughout the system of mathematics. However, in business, we need to be much more careful with the formulas and recognize that usage of letters representing the problems will possibly change from text to text. In looking through different business textbooks, here are two different versions of the same compound interest equation: ( ) These equations are exactly the same but the letters mean something (or possibly nothing) different. While it would be easy to lament the difficulties created by these different versions, realize that our success in business (and life) has as much to do with how well we can see events from other peoples viewpoints. Thus, it is best if when we are presented with these kinds of opportunities, we take the time to develop a better understanding of the other options so that we can better communicate with our colleagues. Comparing ( ) to ( ) what does and represent? Comparing to ( ), describe all of the new variables.

If you answers are not close to $20,000 please reconsider how you are computing the answer.) Bank A = Bank B = Bank C = How do the results compare to your initial guess?

3 Rule of 72: Doubling formula. The rule of 72 is a simple formula designed to quickly approximate the time it takes to double the amount of money in an account which earns a fixed interest rate. In upcoming weeks we will determine how this equation was developed. Yes it is just this simple. Divide the interest rate into 72 and you will have the time it takes for the principle amount to double. In the first problem, the approximate interest rate was 7%, so that the doubling time would be computed as follows: Interest rates are percentages such as 7%. When we place percentages into equations, we have been trained to move the decimal two places. However, in using percentages in the Rule of 72, the rule already accounts for the movement of the decimal point and we do not move the point for this rule.. It is from this equation that we were able to determine the approximate amount of $20,000 was the answer for the first three problems. Compute the approximate doubling time for the following interest rates. 1) 4% 2) 20% 3) 6.5% 4) 2% We will return to the financial math later when it serves a more important purpose. One mathematical area in science where students often struggle is working with formulas that have several variables. For the rest of today we will work with formulas used in science to rewrite the equation. Work the following problem: Solve for x (In other words, rewrite the equation so that we have

Divide the interest rate into 72 and you will have the time it takes for the principle amount to double.

4 Now solve for x It is this second problem which becomes difficult for many students. This difficulty will be overcome through practice. At this time we will present several scientific equations and ask you to solve for a specific variable. 5) solve for 6) solve for 7) solve for 8) solve for 9) [ ][ ] [ ] [ ]

At this time we will present several scientific equations and ask you to

5 10) solve for 11) solve for 12) solve for 13) solve for 14) solve for 15) solve for 16) solve for 17) solve for

Solving Compound Interest Problems

Solving Compound Interest Problems What is Compound Interest? If you walk into a bank and open up a savings account you will earn interest on the money you deposit in the bank. If the interest is calculated