Financial Polynomials

Financial Polynomials 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 œstrikethrough 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. 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 (see problem below) 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. Page 304¦¦¦¦¦¦¦¦..Problem 90 Compounded semiannually. P dollars is invested at annual interest rate r for 1 year. If the interest is compounded semiannually, then the polynomial represents the value of the investment after 1 year. Rewrite this expression without parentheses. Evaluate the polynomial if o Evaluate the polynomial resulting from step 1 using: ? P = $200 and r = 10%, and also with ? P = $5670 and r = 3.5% o Complete problem 70 on page 311 (see problem below) of Elementary and Intermediate Algebra. Show all steps of the division. Page 311¦¦¦¦¦¦¦.Problem 70 (-9×3 + 3×2 “ 15x) ÷ (-3x) 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: o 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 œstrikethrough 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. o 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 Financial Polynomials On page 304, problem #89 states: P dollars is invested at annual interest rate r for 2 years. If the interest is compounded annually then the polynomial P(1 + r)2 represents the value of the investment after 2 years. First we are asked to rewrite the polynomial expression without any parenthesis. This means we need to FOIL the binomial (1 + r)2 and then multiply all terms by P. P(1 + r)2 The original expression P(1 + r)(1 + r) A squared quantity multiplies itself P(1 + r + r + r2) The expression after FOIL was carried out P(1 + 2r + r2) Like terms are combined with r + r = 2r P + 2Pr + Pr2 The P is distributed across the trinomial It could also be noted that unlike traditional polynomials this one is not in descending order of the variable r, but rather in ascending order with the highest exponent in the last term instead of the first term. Now we are to try out our polynomial formula with two different sets of numerical information. Here is the first one: P = $200 and r = 10% = .10 r given as a decimal instead of a percent P + 2Pr + Pr2 The expanded formula 200 + 2(200)(.10) + 200(.10)2 Values are substituted into the formula 200 + 40 + 200(.01) .102 = .01 and 2(200)(.10) = 40 200 + 40 + 2 200(.01) = 2 242 The final result of the formula So $200 left alone for a year at 11% compounded annually results in $242.00. Here is our second set of numerical information: P = $6780 and r = 2.5% = .025 Interest rate as a decimal number P + 2Pr + Pr2 The expanded formula 6780 + 2(6780)(.025) + 6780(.025)2 Values substituted in 6780 + 339 + 6780(.000625) .0252 = .000625 and 2(6780)(.025) = 339 6780 + 339 + 4.2375 6780(.000625) = 4.2375 7123.2375 The final result of the formula Thus starting with $6780 and compounding 2.5% interest once a year yields $343.24 in interest at the end of one year for a total of $7123.24.

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