SOLUTION: 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

Algebra ->  Customizable Word Problem Solvers  -> Finance -> SOLUTION: 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      Log On

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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%.
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Answer by mducky2(62) 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%281%2B+r%2F2%29%5E2
P%281+%2B+r%2F2%29%281+%2B+r%2F2%29
We can use the FOIL method. (Multiply the pairs: front, outside, inside, then last)
P%281+%2B+r%2F2+%2B+r%2F2+%2B+%28r%5E2%29%2F2%29
P%281+%2B+r+%2B+%28r%5E2%29%2F4%29
P+%2B+Pr+%2B+%28Pr%5E2%29%2F4%29

Now we can evaluate this new expression by plugging in P = $200 and r = 0.1 (10% equals 10/100 or 1/10):
P+%2B+Pr+%2B+%28Pr%5E2%29%2F4%29
200+%2B+200%280.1%29+%2B+200%280.1%29%5E2%2F4
200+%2B+20+%2B+200%2A0.01%2F4%29
220+%2B+2%2F4%29
220+%2B+1%2F2%29
220.5

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