MATH106: Introduction to Formulas

Formulas are models of problem solutions. In Module 1, you learned how to evaluate and manipulate formulas from many different application areas. This allows you to use a formula in many ways. Specifically, if there are n variables in the formula, there are n different representations of it. You can solve any of the n variables in terms of the (n-1) other variables to solve even more problems without rethinking the process. Thus, formulas allow you to reach solutions more quickly. Formulas can help you predict solutions also. This module week, you will work with a specific formula to investigate what happens when a variable value in the formula is changed. Recall that I = PRT is the formula for simple interest where I is the simple interest accumulated from multiplying the original amount of money, Principal, by the interest rate per year given as a percent, and Time, in years. The total amount of money, A, you accumulate at the end of T years, if you are saving money, is given by the formula A = P + I. This is the same formula for the amount of money you have paid back on a loan after T years. Borrowing and saving money are things you are going to do throughout life. This formula is only the tip of the iceberg for financial literacy. Let’s have some fun with it! Before taking out a loan, it is essential to know the repayment terms and how your interest rate and the time of the loan affect the total loan balance. For simplicity in this assignment, assume each monthly payment contains an equal principal and interest amount. In this discussion, you will examine how a formula is used to explain the effects of changing variable values. Please proceed to the Prepare section.

Prepare

• Think of a big-ticket item you might need to take out a loan to purchase. Dream big! What have you always wanted? This could be a boat, car, motorcycle, or a trip around the world, but not a house. (A house loan has many other considerations.) Research the cost of this item and be sure to bookmark the link.
• Review the terminology from pages 132-133 of the textbook if necessary. Think about any computational sub-steps that need to be taken. Note that in simple interest, the monthly payment is the same each month.
• Select a reasonable interest rate for your item (between 2% and 10% is standard). It does not have to be a whole number. Then, select a time period to pay off your loan (between 3 and 12 years is common). It is standard to be a whole number.
• Please proceed to the Initial Post section.

Initial Post

For your initial post, respond to the following prompts.

1. Describe the item you are taking a loan out for and state the purchase price. For purposes of the assignment, assume the price includes all taxes, etc.
2. Include the direct URL so your peers can view your big-ticket item.
3. Using the simple interest formula, state your chosen interest rate and amount of time for your loan.
4. Show the formula with numbers and describe the steps to compute the interest on the loan, I, and the total amount of the loan, A. You may use a calculator to perform the computations.
5. Think about it, then show the equations with numbers and describe the steps to compute the monthly payment, M, for the life of the loan. You may use a calculator to perform the computations.
6. Explain one way to verify your monthly payment is correct. Show the formula and use a calculator for the computations.
7. Submit your initial post to the discussion by the fourth day of the module week. You must make your initial post before you can see your classmates’ posts.

Please proceed to the Response Prompts section.