Question 165922
Compounded semi-annually. P dollars is invested at annual interest rate r for 1
 year. If the interest is compounded semi-annually, then the polynomial p(1+r/2)^2
 represents the value of the investment after 1 year. 
:
Rewrite this expression without parenthesis.
A = p(1+r/2)^2
:
FOIL (1+(r/2))*(1+(r/2)) to get rid of the exponent
A = p *(1 + {{{2(r/2)}}} + {{{r^2/4}}})
:
A = p (1 + r + {{{r^2/4}}}); cancel 2
:
Multiply what's inside the brackets by p
A = p + pr + {{{(pr^2)/4}}}
: 
Evaluate the polynomial if P= $200 and r =10%.
Substitute for p and r in the above equation
:
A = 200 + 200*.10 + {{{(200*.1^2)/4}}}
:
A = 200 + 20 + {{{(200*.01)/4}}}
:
A = 220 + {{{2/4}}}
:
A = 220 + .50
:
A = 220.50
:
:
Check solution on a calc: enter 200*(1+(.1/2))^2 = 220.5