Running Head: FINANCIAL POLYNOMIALS
Running head should use a shortened version of the title if the title is long! All capital
letters for the title and the words Running and Head should be capitalized as well.
Financial Polynomials (full title; centered horizontally & vertically)
First Name Last Name
MAT 221
Dr. XXXXXXXXX XXXXXXX
Date
1
FINANCIAL POLYNOMIALS
2
Financial Polynomials
Be sure to have a centered title on page 1 of your papers!!
[The introductory paragraph must be written by each individual student and the content will vary
depending on what the student decides to focus on in the general information of the topic. YOUR
INTRODUCTION SHOULD CONNECT MATH CONCEPTS AND REAL-WORLD
APPLICATIONS. DO NOT INCLUDE THE DIRECTIONS IN THE INTRO! The following
paragraph is not an introduction to the paper but rather the beginning of the assignment.]
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” (Dugopolski, 2012). [This quote has less than 40 words so it
does not need block quote.] The first part requires the polynomial expression to be rewritten
without any parentheses. This means FOIL, or multiply First, Outer, Inner, Last, the binomial (1
+ r)2 and then multiply all terms by P.
P(1 + r)2
The original expression with the exponent ONLY with the binomial
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. Additionally, this is an expression and not an equation so a solution for the
variables cannot be found unless given values to use.
Next, the polynomial formula with two different sets of numerical information will be
solved. In these types of problems, a single numeric value will be found that represents the total.
1. P = $200 and r = 10% = .10
r given as a decimal instead of a percent
FINANCIAL POLYNOMIALS
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P + 2Pr + Pr2
The expanded formula
200 + 2(200)(.10) + 200(.10)2
Values are substituted into the formula
200 + [400(.10)] + [200(,01)]
Exponents and Multiplication
200 + 40 + 2
Finish order of operations with addition
242
The final result of the formula
According to the formula, $200 left alone for a year at 11% compounded annually results
in $242.00.
Here is the second set of numerical information:
P = $6780 and r = 2.5% = .025
P + 2Pr + Pr2
Interest rate as a decimal number
The expanded formula
6780 + 2(6780)(.025) + 6780(.025)2 Values substituted in
6780 + 339 + 4.2375
Order of operations and decimal rules used.
7123.2375
The final result of the formula
This value must be rounded since numbers beyond the hundredths column do not apply in the
existing currency system. 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.
The final part of the assignment involves simplifying a polynomial expression. To do
this, like terms, distributive property, and order of operations must be used.
(8y4 – 6y3 – 2y) ÷ (–2y)
The original expression
8y4 – 6y3 – 2y
Rewrite it so that it is clear what is being divided.
–2y
8y4 -6y3 -2y
–2y –2y –2y .
Each term must be divided by the denominator.
FINANCIAL POLYNOMIALS
–4y3 + 3y2 + 1
4
Simply each term.
When variables with exponents are divided, we subtract the exponents. The numbers are divided
as usual. Evaluate the + and – signs, also. Since these terms are not alike, they cannot be
combined so the answer is simplified.
[The conclusion paragraph must be written by each individual student and the content will vary
depending on what the student decides to include in their summary. DO NOT INCLUDE
PERSONAL NARRATIVE LIKE “I LEARNED…” OR “WE CAN DO….”. BE SURE TO
SUMMARIZE WHY THE CONCEPT(S) ARE IMPORTANT AND HOW THEY CAN BE
CONNECTED TO OTHER CONCEPTS.]
FINANCIAL POLYNOMIALS
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Reference
Dugopolski, M. (2012). Elementary and intermediate algebra (4th ed.). New York, NY:
McGraw-Hill Publishing.
Use the word ‘Reference’ or ‘References’ as the title. THERE IS NO COLON OR
UNDERLINE.
Textbook should ALWAYS be included in every assignment! Be sure to use appropriate
indentation (hanging), font (Arial or Times New Roman), and size (12).
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