SOLUTION: Hi I need help with a word problem involving interest rates Please. P dollars is invested at annual interest rate r for 1 year. If the interest is compounded semiannually, then

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Question 203315: Hi I need help with a word problem involving interest rates Please.
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
represents the value of the investment after 1 year. Rewrite this expression
without parentheses. Evaluate the polynomial if
P= $200 and r= 10%.
My Try: I know I have to substitute the numbers in for the variables, but not sure how to solve after that. 200(1+10%/2)^2 = 200+220/2=110^2=220??
Thanks
Found 2 solutions by MathTherapy, Earlsdon:
Answer by MathTherapy(10551) About Me  (Show Source):
You can put this solution on YOUR website!
Value of investment after 1 year = P%281%2Br%2F2%29%5E2

Rewriting the expression without parentheses, we get:

P%281%2Br%2F2%29%281%2Br%2F2%29 = P%2A%281%2B%28r%2F2%29%2B%28r%2F2%29%2B%28r%5E2%2F4%29%29

P%2A%281%2B%282r%2F2%29%2B%28r%5E2%2F4%29%29 = P%2B%282Pr%2F2%29%2B%28Pr%5E2%2F4%29%29

%284P%2B4Pr%2BPr%5E2%29%2F4

Evaluating the polynomial without parentheses, we get:

Value of investment after 1 year = %284P%2B4Pr%2BPr%5E2%29%2F4, where P = $200, and r = 10%, or .1

%284P%2B4Pr%2BPr%5E2%29%2F4 = %28%284%2A200%29%2B%284%2A200%2A.1%29%2B%28200%2A%28.1%5E2%29%29%29%2F4

= %28800+%2B+80+%2B+2%29%2F4 = 882%2F4 = $highlight_green%28220.50%29

Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
P%281%2Br%2F2%29%5E2
1) Rewrite the expression without parentheses.
P%281%2B2%28r%2F2%29%2Br%5E2%2F4%29 Distribute the P.
highlight%28P%2BPr%2BPr%5E2%2F4%29
2) Evaluate if P= $200 and r = 10% (or 0.1 in its decimal form).
200%2B200%280.1%29%2B200%280.1%29%5E2%2F4+=+200%2B200%280.1%29%2B200%280.01%29%2F4=200%2B20%2B2%2F4+=+highlight%28220.5%29