Financial Polyminals

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This week’s assignment focused on polynomials, binomials, and monomials. We were provided with the polynomial expression to solve. Our textbook, Elementary, and Intermediate Algebra (2012), I need to solve for problem 70 on page 304. The textbook explained that P dollars is invested at annual interest rate r for 1 year. If the interest is compounded semiannually, then the polynomialP(1+r/2)^2 represents the value of the investment after 1 year. Our assignment is to solve this expression without parentheses. My first step is rewriting the expression getting rid of parentheses. I start with my original expression which is, P(1 + r/2)2 This is my original expression P(1 + r/2)(1 + r/2) A squared quantity multiplies itself P(1 + r/2 + r/2 + r2/4) The expression after FOIL was carried out P(1 + r + r2/4) My next step is to combine like with r/2 + r/2 = r P + Pr + Pr2/4 The trinomial is distributed across

My next step is to plug in my numbers provided for the assignment, which P = $200 and r = 10%.

P + Pr + Pr2/4 The expanded formula 200 + 200(.10) + 200(.10)^2/4 Values are substituted into the formula 200 + 20 + 200(.10)^2/4 .10^2= 0.01 and 200(0.01) = 2 200 + 20 + 200(0.01)/4 2/4= 0.5

200 + 20 + 0.5
220.05 My answer is 220.05 So $200 left alone for a year at 1% compounded semiannually results in $220.05 in 2 years.

My next expression, I solved for P = $5670 and r = 3.5%.
5670 + 5670(0.35) + 5670(0.35)^2/4 Values are substituted into the formula 5670 + 1984.5 + 5670(0.35)^2/4 Multiplication and squaring are completed 5670 + 1984.5 + 3969/4 Adding and dividing is next...
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