Financial Polynomials
MAT 221
Professor Nikita Echols September 29, 2014

Introduction The goal in evaluating the polynomials in this assignment is to figure out what the interest rate, the number of years, whether it will be annually or semi-annually, and the initial amount invested. Knowing how much money is invested, the interest rate and the number of years will determine how much interest is gained. On this assignment we are using a compounded semiannual equation. P(1+r/2)2. We will need to rewrite the polynomial expression without the parenthesis. So our binomial is (1+r/2)2 and it will be multiplied by P.
The binomial is simplified by multiplying itself from squared
P(1+r/2)(1+r/2)
The acronym, FOIL (First, outer, inner, last) will be used next
P(1+r/2+r/2+r2)
After FOIL has been applied, like terms will be combined together. r/2+r/2 = 2r/2
P(1+2r/2+r2)
Then P will be added to the trinomial
P+2Pr/2+Pr2
The expression is now P(1+r/2)2. We already have the given numbers P = 200 and r = 10%. The rate will be used by the divisor of 2 because it will be compounded semiannually. We will plug in the information given to P+2Pr/2+Pr2.
200 + 2(200)(.10/2) + 200(.10)2
The given numbers will be substituted into the formula
200 + [400(.10/2)] + [200(.01)]
Divide the values in parentheses first then multiply everything to simplify
200 + 20 + 2
Once everything has been simplified add everything to finish the order.
The final number will be 222. With the formula and $200 left for half a year at 10% compounded semiannually we will have acquired $22 of interest making a total of $222.00. The second set of numbers that we have been given are:
P = 5670 and r = 3.5% = .035
Plugging in the numbers from above will give us the expanded formula using: P + 2Pr/2 + Pr2
5670 + 2(5670)(.035/2) + 5760(.035)2
All the given values are substituted
5670 + 198.45 + 7.056
After doing the expressions everything will be added
The final result will be 5875.51. Next the value must be rounded to 5875.51. With the interest rate at 3.5% the compounded semiannual incurred amount will be $115.51 making the total