MAT 221: Introduction to Algebra

Financial Polynomials

Problem 90 on page 304 of the text book shares the steps and formula needed to square the binomial and multiplication for the Compounded semiannually. (Dugopolski, 2012) Using the formula provided, as well as the problems assigned, I will calculate the math to find the interest rate on an investment. This will help me in real life understand how to calculate interest on future savings. I will show all steps of the squaring of the binomial and multiplication along with any simplification which might be required to solve as I work through the math.

An expression containing numbers and variables grouped according to certain patterns is a polynomial. (Dugopolski, 2012) Like whole numbers, polynomials may be prime or factorable into products of primes. In the text the following expressions were given; P=$200 and r= 10%, and P=$5670 and r=3.5%.

To begin the math, first I will rewrite the expression without the parenthesis. This means FOIL, or multiply First, Outer, Inner, Last, the binomial:

P(1+r/2)²

P(1+r/2)* (1+r/2)*

P(1+r/2 + r/2+r²/2)

P(1+r+r²/4)

P + Pr+Pr²/4

Next I’ll evaluate the new expression by entering the figures provided in the assignment. P = $200 and r = 0.1 (10% equals 10/100 or 1/10):

P + Pr + Pr²/4

200 + 200 * (0.1) + 200*0.1)²/4

200 + 20 + 200*0.01/4

Then I will simplify

220+2/4

Reduce to the lowest terms

220+1/2

$220.50 This is the answer. This is the value of the investment after one year.

The 2nd set of calculations:

P = $5670 and r = 3.5% = .035 Interest rate as a decimal number

P + 2Pr + Pr2 The expanded formula

5670 + 2(5670)(.035) + 5670(.035)2

P = $5670 and r = 3.5% = .035 The interest rate with decimals

P + 2Pr + Pr2 expanded formula

5670 + 2(5670)(.035) + 5670(.035)2 The expanded equation with values entered

6073.84475 The answer or $6,073.84 is the rounded answer