SOLUTION: P dollars is invested at annual interest r for 1 year. If the interest is compounded semiannually, then the polynominal P ( 1 + r/2) ^2 represents the value of the investment after

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: P dollars is invested at annual interest r for 1 year. If the interest is compounded semiannually, then the polynominal P ( 1 + r/2) ^2 represents the value of the investment after      Log On


   

Question 221415: P dollars is invested at annual interest r for 1 year. If the interest is compounded semiannually, then the polynominal P ( 1 + r/2) ^2 represents the value of the investment after 1 year. Rewrite this expression without parentheses. Evaluate the polynominal if p= 200 r=10%
I am not sure how to begin to solve this equation. PLEASE PLEASE HELP!!!
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
P%281%2Br%2F2%29%5E2 Start with the given expression.


P%281%2Br%2F2%29%281%2Br%2F2%29 Expand


P%281%2A1%2B1%2A%28r%2F2%29%2B%28r%2F2%29%2A1%2B%28r%2F2%29%28r%2F2%29%29 FOIL


P%281%2Br%2F2%2Br%2F2%2Br%5E2%2F4%29 Multiply


P%281%2B2r%2F2%2Br%5E2%2F4%29 Combine like terms.


P%281%2Br%2Br%5E2%2F4%29 Reduce


P%2BPr%2BPr%5E2%2F4 Distribute


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200%2B200%2A0.1%2B%28200%2A0.1%5E2%29%2F4 Plug in P=200 and r=0.1 (the decimal equivalent of 10%).


200%2B200%2A0.1%2B%28200%2A0.01%29%2F4 Square 0.1 to get 0.01


200%2B20%2B2%2F4 Multiply


200%2B20%2B0.5 Divide


220.5 Combine like terms.


So P%2BPr%2BPr%5E2%2F4=220.5 when P=200 and r=0.1


This also means that P%281%2Br%2F2%29%5E2=220.5 when P=200 and r=0.1