Financial Polynomials

Read the following instructions in order to complete this assignment and review the example of how to complete the math required for this assignment:

1. Solve problem 90 on page 304 of Elementary and Intermediate Algebra. Be sure that you show all steps of the squaring of the binomial and multiplication along with any simplification which might be required.
   
   
   • Evaluate the polynomial resulting from step 1 using:
     
     
     • P = $200 and r = 10%, and also with
       
       
     • P = $5670 and r = 3.5%
       
       
   • Complete problem 70 on page 311 of Elementary and Intermediate Algebra. Show all steps of the division.
     
     
2. Write a two- to three-page paper that is formatted in APA style and according to the Math Writing Guide. Format your math work as shown in the Instructor Guidance and be concise in your reasoning. In the body of your essay, please make sure to:
   
   
   • Demonstrate your solution to the above problems, making sure to include all mathematical work and a discussion of how and why this is applicable to your everyday life.
     
     
     • Use the underline feature with single spacing to set up the division(s), and use the “strikethrough” font to show the canceling factors. Can you think of another way this division could be approached and worked out? If yes, briefly describe the method.
       
       
   • Incorporate the following five math vocabulary words into your discussion. Use bold font to emphasize the words in your writing (Do not write definitions for the words; use them appropriately in sentences describing your math work.):
     
     
     • FOIL
       
       
     • Like terms
       
       
     • Descending order
       
       
     • Dividend
       
       
     • Divisor

 

 

Discussion Week 4

Read the following instructions in order to complete this discussion, and review the example of how to complete the math required for this assignment:

1. Think of something you want or need for which you currently do not have the funds. It could be a vehicle, boat, horse, jewelry, property, vacation, college fund, retirement money, or something else. Pick something which cost somewhere between $2000 and $50,000.
2. On page 270 of Elementary and Intermediate Algebra you will find the “Present Value Formula,” which computes how much money you need to start with now to achieve a desired monetary goal. Assume you will find an investment which promises somewhere between 5% and 10% interest on your money and you want to purchase your desired item in 12 years. (Remember that the higher the return, usually the riskier the investment, so think carefully before deciding on the interest rate.)
3. State the following in your discussion:
   • The desired item
   • How much it will cost in 12 years
   • The interest rate you have chosen to go with from part 2
4. Set up the formula and work the computational steps one by one, explaining how each step is worked, especially what the negative exponent means. Explain what the answer means.
5. Does this formula look familiar to any other formulas you are aware of? If so, which formula(s) and how is it similar?
6. Incorporate the following five math vocabulary words into your discussion. Use bold font to emphasize the words in your writing (Do not write definitions for the words; use them appropriately in sentences describing your math work.):
   • Power
   • Reciprocal
   • Negative exponent
   • Position
   • Rules of exponents

Your initial post should be 150-250 words in length. Respond to at least two of your classmates’ posts by Day 7. Do you agree with how they used the vocabulary? Do their answers make sense?

 

 

INSTRUCTOR GUIDANCE EXAMPLE: Week Four Discussion

 

Initial Investment

My best friend and her new husband (Fred and Ethel) just got back from their honeymoon which was a trip down the River Nile in Egypt. They are excited about traveling together as a couple and they want to start saving for a very special trip. My own 25

th wedding anniversary falls in the same month as Fred and Ethel’s 12th anniversary and they thought it would be fun to plan a trip together. They have done a little research enough to realize we will need about $8,000 per couple set aside for this trip. Fred also found an investment opportunity which promises to have an average return of about 9% per year if one invests long term. We need to know how much each couple needs to invest now to reach their goal in time.

 

The desired item is travel.

 

The cost in 12 years will be about $8,000.

 

The average interest rate of the investment is 9%.

 

The Present Value Formula is P = A(1 + r)

-n where P is the present value that will amount to A dollars in n years at interest rate r compounded annually.

 

Notice that the quantity raised to a

power has the negative exponent of –n. According to the rules of exponents, this means that once the negative is put into effect, the base quantity will change position by dropping down into the denominator where it will be raised to the power of n. Then it will divide A instead of multiplying A as it seems to be doing now.

 

P = A(1 + r)

-n

 

P = 8000(1 + .09)

-12 Here are the relevant numbers are plugged into the formula

 

P = 8000(1.09)

-12 Add inside the parenthesis

 

P = 8000 The

negative exponent creates the reciprocal of the base number

 

(1.09)

12 (in other words, changes its position from up top to down below)

 

P = 8000 The exponent is applied to the base number

 

2.81266…

 

P = 2844.28 This is the value of P using the formula.

 

Given these results and knowing the interest rate may not stay exactly at 9% we will begin our investment with $3000 right now to begin to save for our big twenty-fifth (and twelfth) anniversary trip. This should give us a little cushion for inflation and such

 

 

Lab for Week 5.