Financial Polynomials
Gail Frazier
MAT221
Instructor Elizabeth Stepp
August 29, 2013
Polynomial appears in financial context, and allows me to be able to practice analyzing information presented in a non linear format. Because of the rules, polynomials are easy to work with and easy to simplify, because like terms can be combined. Fractions are used in financial planning. P dollars is invested at annual interest rate for one year. If the interest is compounded semiannually then the polynomials P (10%) represents the value if the investment after one year. First, we are asked to rewrite the polynomial expression without any parentheses. This means we need to Foil the binomial (10%) and then multiply all terms by P.
1 + t) 2 or r/3r²/3 Rewrite without parenthesis 3
P 10% The original expression
P (10 +10)+ (10+10) A square quality multiples it
P (10 +10) The expression after Foil was carried out
P (10) Like terms are combined with 10 + 10= r
P + Pr + Pr 2/4 The P is distributed across the trinomial It could also be noted that the unlike rational polynomials has one that is not in descending order of the variable r, but rather in ascending order with the highest exponent in the term instead of the first term. Now we are to try our polynomial formula with two different sets of numeral information. Here is the first one:
P= $200 and r + 10% = .10 Given as a decimal instead of percent
P + Pr + Pr 2/4 The expanded formula
200 + 200 (.10) + 200 (.10) ²/4 Values are substituted into the formula
200-20 + 200 (0.4)/4 .10² + 0.4 and 200 (0.4) = 0.4
200 + 200 (.10) + 200 + (.10) 200 (.0.01) + 10
200 + 200 (.10) + 5
$220.5 The result of the formula is $200 left alone for the year at 10% compounded semiannually results in $220.5
Here is the second set of numerical information:
P + $5670 an v + 35%= 0.0350 Interest rate is a decimal number
P= Pr + Pr ²/4 The expanded formula
5670+ 5670 (.0350) = 5670 (0.0350) ²/4 Values substituted in
5670 +198.45 + 5670 (0.00875)/4 The first multiplication and squaring done
5870.186437 Additions then last multiplication and division done
5870.186437 The final result of the formula Thus starting with $5670 and compounding 3.5% interest twice a year yields, $198.45
