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M4D1: Consolidating Student Loans

In this discussion, you will work in small groups in online discussions to solve a mathematics problem involving consolidating two student loans into one combined loan. This group discussion will help prepare you for activity M4A2, in which you will write and submit an individual complete solution to a related problem.

Answer the following questions.

Suppose you have two student loans:

  • $15,000 with an APR of 8% for 15 years
  • $10,000 with an APR of 9.5% for 20 years
    1. Calculate the monthly payment for each loan individually.
    2. How much do you pay each month? How long do you have to pay that monthly amount?
    3. Over the course of each loan, how much total do you pay? How much of that is interest? How much interest will you pay in total?

You have the opportunity to consolidate these 2 loans into a single loan with an APR of 8% and a term of 12 years.

  1. What will be your monthly payment if you consolidate?
  2. How does that payment compare with what you are paying on the two loans individually? Does this result make sense to you? Why or why not?
  3. What will your total payments be over the life of the loan? How much of that is interest?
  4. What are the pros and cons of doing this consolidation?

Be sure to answer all parts of the question above. It is possible that you will not be successful at answering all parts of the question at this point, and that is okay. Describe what you were able to solve and what questions you have remaining.

This is intended to be a challenging problem that will require you to work together for a successful solution. Just as you learn from others' ideas, they will learn from your questions and contributions. Whether you understand a complete solution to the problem or are struggling to work it through, you are expected to participate actively in the discussion throughout the module and to work collaboratively with your classmates on a thorough problem solution.

Goals for this discussion, while working with your classmates:

  • The focus here is not only on finding the "right" answers, but on explaining and justifying your reasoning for all mathematical steps and ideas you present.
  • Engage with and reflect on the issues being discussed, which will be critical for your course grade.
  • Demonstrate that you understand all parts of the problem and its solution by the end of the module

This will prepare you for the next activity, in which you will write and submit an individual complete solution to a similar problem.

To earn the maximum number of points for this discussion:

  • Your solution postings:
    • For you initial posting, create a new discussion thread with a solution attempt or a question to help you get started. Your initial post is due by Tuesday for the 8-week course or Thursday of the first week for the 15-week course.
    • Present a complete solution to all parts of the problem by the end of the Module.
    • Show your justification for every step in your solution, using clear mathematically-accurate language. You can use phrases to explain your reasoning step-by-step, but clearly state your final conclusions using complete English sentences (for example, “Jill needs to add 43 gallons of water to her pool.”)
    • Label all numbers with the units they represent (e.g. 0.3048 ft/meter).
  • Your responses to your groupmates:
    • Post at least three (3) separate days throughout the module, with a total of at least six (6) thoughtful responses to others.
    • Communicate clearly. Do not use abbreviations common in texting.
    • At least 4 of your posts must make important contributions to solving or understanding the problem. This can include your initial posting. These posts must be relevant, unique (not repeating ideas from someone else's post), and justified (you explain your reasoning in a way that others can understand). You do not need to write extensively, but contribute thoughtfully in ways that help us all learn about important mathematical ideas. Thoughtful questions are valid contributions.
  • All your postings:
    • Please use the equation editor within the Discussion Board so your mathematics is clear to your instructor and fellow students. Here is a Blackboard Equation Editor Tutorial [Video file. 12:06 mins]. Watch segments 0-3:30 and 4:20-4:45. Segment 6:55-11:52 is also useful.
    • To cancel units, please refer to these Directions to Cancel Units in BB Equation Editor [DOC file, size 1.6 MB].
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