**This is a graded discussion: 100 points possible**

**due Dec 4**

Module 2 Discussion: A Formula Investigation

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Module2A Formula Investigation

Discussion

Please read through all sections before proceeding to the next page and refer back whenever necessary.

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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 will affect the total loan balance. For simplicity, you are using the flat rate method where each monthly payment contains an equal principal and interest amount. This is not an amortization problem.

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.

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.

For your initial post, respond to the following prompts.

· 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.

· Include the direct URL so your peers can view your big-ticket item.

· Using the simple interest formula, state your chosen interest rate and amount of time for your loan.

· 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.

· Think about, 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.

· Explain one way to verify your monthly payment is correct. Show the formula and use a calculator for the computations.

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.

Read a selection of your classmates’ postings and reply to **at least two** using the following prompts. Your replies should address all parts of the prompt and be completed by **the** **seventh day of the module week.**

Reply 1

Respond to at least one classmate’s initial post by answering the following:

· Think about then show the formula with numbers for what happens to the interest, the total amount of a loan, and monthly payments of your classmate’s loan if the **time** was reduced by one and a half years at the start of the loan. You may use a calculator to perform the computations.

· Explain why your classmate will pay a different amount (more or less) for the loan in the end. Were you surprised by the results? Why or why not?

· If this was your loan and dream object, discuss one change you could make in your life to make the new monthly payment possible. What would you expect to happen if the **time** was increased at the start of your classmate’s loan? Why?

Reply 2

Respond to a different classmate’s initial post by answering the following:

· What do you think will happen if the interest **rate** provided in your classmate’s post was decreased by one percentage point at the start of the loan? Explain why.

· Confirm your answer. Show the formula with numbers and compute the new interest your classmate will pay with this new interest rate. You may use a calculator to perform the computations.

· Compare the interest of the two loans. Share with your classmate how much interest will be saved over the loan length.

Review the Discussion Rubric for detailed grading information.

Please proceed to the **Why?** section.

General Education Competencies

*Critical Thinking*

The student will apply knowledge at the synthesis level to define and solve problems within professional and personal environments.

*Quantitative Reasoning*

The student will demonstrate the use of digitally enabled technology (including concepts, techniques, and tools of computing), mathematics proficiency and analysis techniques to interpret data for the purpose of drawing valid conclusions and solving associated problems.