Financial Polynomials
A polynomial is a mathematical expression consisting of a sum of terms, each term including a variable or variables raised to a power and multiplied by a coefficient. The simplest polynomials have one variable but they can have two three or more variables. Knowing the formula and how to use and brake down polynomial can help us in our everyday lives. It can help you figure out how much interest you can accrue from a deposit or investment that you made with a given interest rate. Let’s take a closer look at an equation that deals with polynomials.
“P dollars is invested at annual interest rate r for 1 year. If the interest is compounded annually then the polynomial P(1 + r)2 represents the value of the investment after 1 year” (Dugopolski, 2012).
P(1 + r/2)2 Original expression
P(1 + r/2)(1 + r/2) Simplify the expression by using foil this means multiply first outer,
Inner, last
P(1+ r/2 + r/2 + r2/4) Combine the like terms
P(1 + 2(r/2) + r2/4) Distribute P across the trinomial
P + Pr + Pr2/4 Put all variables in descending order
Now let’s try our formula with a given set of numerical information P=200 r =10% interest rate .10 as a decimal.
P + Pr + Pr2/4 expanded formula
200 + 2/4(200)(.10) + 200(.10)2 substitute values into formula
200 + 10 + 200(.01) multiply
200 + 10 + 2 add
212 answer
This means that $200 left alone to collect interest for one year with an interest rate of 10% would be $212.
The second equation is solve for P=$5670 r=3.5%
P = $5670 and r = 3.5% = .035 interest rate as a decimal
P + 2Pr + Pr2...