Questions on Word Problems: Money, Business and Interest answered by real tutors!

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Question 152830: D -92: Compounded semiannually. P dollars is invested at annual interest rate r for 1 year. If the interest is compounded semiannually, then the polynomial P(1+ r/2)2 (the r and 2 is in fraction from and the 2 outside the parentheses is a degree) represents the value of the investment after 1 year. Rewrite this expression without parentheses. Evaluate the polynomial if P=$200 and r= 10%.
I was unable to locate ISBN
: D -92: Compounded semiannually. P dollars is invested at annual interest rate r for 1 year. If the interest is compounded semiannually, then the polynomial P(1+ r/2)2 (the r and 2 is in fraction from and the 2 outside the parentheses is a degree) represents the value of the investment after 1 year. Rewrite this expression without parentheses. Evaluate the polynomial if P=$200 and r= 10%.
I was unable to locate ISBN

Answer by mducky2(55) About Me  (Show Source):
You can put this solution on YOUR website!
Let's start with the first part of the question, which is rewriting the expression without parentheses.
P(1+ r/2)^2
P(1 + r/2)(1 + r/2)
We can use the FOIL method. (Multiply the pairs: front, outside, inside, then last)
P(1 + r/2 + r/2 + (r^2)/2)
P(1 + r + (r^2)/4)
P + Pr + (Pr^2)/4)

Now we can evaluate this new expression by plugging in P = $200 and r = 0.1 (10% equals 10/100 or 1/10):
P + Pr + (Pr^2)/4)
200 + 200(0.1) + 200(0.1)^2/4
200 + 20 + 200*0.01/4)
220 + 2/4)
220 + 1/2)
220.5

Therefore, the value of the investment after one year is $220.50.