Compounded Semiannual Interest
Ashford University
MAT 221
Compounded Semiannual Interest
In this paper we are given three problems to figure out. Two of these problems entail the use of compound interest, with the other problem dividing two polynomials. Through this paper we will discuss the steps needed in which to solve these problems. The following formula will be used P(1 + r/2)^2. With the fact that this has an exponent, we must remove this exponent to get an accurate answer. We will now set the formula up to (1 + r/2) * (1 + r/2). Using the foil method we will use multiplication. We will use (A + B)*(C + D) = (1 + r/2)*(1 + r/2) where A = 1, B = r/2, C = 1, and D = r/2. When A is multiplied by C, it basically boils down to 1 multiplied by 1 which results in 1. From there we will multiply A by D which is 1 times r/2, and that equals r/2. Last we will multiply B by D which would result in r/2 multiplied by r/2. The result of this is two fractions is the result of the product of the terms of the numerator is R and R which comes to r squared because there are two of R’s. The product of the two denominators is 2 times 2 which come to 2 squared. The squared becomes 4. So when everything is put where it needs to be it should create the fraction r squared over 4, or r^2/4. When one uses the foil method, it creates AC + AD + BC + BD which is the same as 1 + r/2 + r/2 + r^2/4. If one noticed, r/2 and r/2 are the same, or like terms which causes them to be added together.
If you think of the R as a possible 1 it could make one think of r/2 as a ½ which would make both of those equal 1. Now placing R back into the equation it would create 1 + r + r^2/4 = 1 + r + 0.25r^2 where 1/4 is equal to 0.25. Now you can multiply the equation by P to get P + Pr + 0.25Pr^2.
The word problem which we have states that we must find the amount after 1 year for $200 which has an annual interest of 10% which is compounded semiannually.