Financial Polynomials

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MATT 221

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Financial Polynomials

Polynomials are expressions that involve more than two algebraic terms especially sum of various terms which contain different powers but of the same variable. The word comes from ‘poly-‘meaning many and ‘nomial’ meaning terms. Financial polynomials are expressions that are used to calculate the present or values of funds. They are mostly used by people who engage in fund management for example in banks and insurance firms. Its importance can never be overestimated.

‘‘P dollars is invested at annual interest rate r for I year. If the interest is compounded semiannually, then the polynomial P (1 + r/2)2 represents the value of the investment after I year. Rewrite this expression without parentheses. Evaluate the polynomial if P: $200 and r – l0%-’’ (Dugopolski, 2012). The instruction is that the expression is to be rewritten without parenthesis. This means FOIL and then multiplies all the terms by P.

P (1 + r/2)2 this is the original expression with the exponent

P (1 + r/2) (1 + r/2)the squared quantity the multiplies itself

P (1 + r/2 + r/2 + r2/4) the result due to carrying out FOIL

P (1 + 2r/2 + r2/4)like terms are combined that is r/2 + r/2 = 2r/2

P + 2Pr/2 + Pr2/4the P is distributed across the trinomial

The polynomial is not in descending order as it has the highest exponent in the last term instead of the first term so it is in an ascending order. This is an expression and not an equation so a solution for the variables cannot be found unless given values to use.

Then 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

P + 2Pr/2 + Pr2/4 the expanded formula

200 + 2(200) (0.10)/4 + 200(0.10)2/4 values are substituted into the formula

200 + 400(0.10) /4+ 200(0.01) /4 exponents and Multiplication

200 + 10 + 0.5 Finish order of operations with addition

210.5 The final result of the formula

Therefore $200 left alone for a year at 11% compounded annually results in $210.50 according to the formula.

The second set of numerical information gives us the following working:

P = $6780 and r = 2.5% = .025 Interest rate as a decimal number

P + 2Pr/4 + Pr2/4the expanded formula

6780 + 2(6780) (.025)/4 + 6780(.025)2/4 values substituted in

6780 + 84.75 + 1.059375 Order of operations and decimal rules used.

6865.8094 The final result of the formula

Starting with $6780 and compounding 2.5% interest once a year yields $85.8094 in interest at the end of one year for a total of $6865.8094.

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

(-9×3 + 3×2 – 15x) ÷ (-3x)the original expression

(-9×3 + 3×2 – 15x) rewrite the equation for clarity

-3x

-9×3 + 3×2 – 15xdivide each term by the denominator

-3x -3x -3x

3×2 + x + 5 the final answer

In summary, the application of financial polynomials has helped calculate the future values of funds given the interest rates. Given the principal and the interest rates, one is able to determine the future value of the fund depending on the time frame given for the investment using the formula P (1 + r)2 . The polynomials ensure that there is accuracy when making these calculations. Bankers, insurers, mortgage institutions among others will always need financial polynomials to succeed in their fields.

Reference

Dugopolski, M. (2012). Elementary and intermediate algebra (4th Ed.). New York, NY: McGraw-Hill Publishing.

Krause, E. F. (2012). Taxicab geometry: An adventure in non-Euclidean geometry. Courier Dover Publications.