Question 221415
{{{P(1+r/2)^2}}} Start with the given expression.



{{{P(1+r/2)(1+r/2)}}} Expand



{{{P(1*1+1*(r/2)+(r/2)*1+(r/2)(r/2))}}} FOIL



{{{P(1+r/2+r/2+r^2/4)}}} Multiply



{{{P(1+2r/2+r^2/4)}}} Combine like terms.



{{{P(1+r+r^2/4)}}} Reduce



{{{P+Pr+Pr^2/4}}} Distribute



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{{{200+200*0.1+(200*0.1^2)/4}}} Plug in {{{P=200}}} and {{{r=0.1}}}  (the decimal equivalent of 10%).



{{{200+200*0.1+(200*0.01)/4}}} Square 0.1 to get 0.01



{{{200+20+2/4}}} Multiply



{{{200+20+0.5}}} Divide



{{{220.5}}} Combine like terms.



So {{{P+Pr+Pr^2/4=220.5}}} when {{{P=200}}} and {{{r=0.1}}}



This also means that {{{P(1+r/2)^2=220.5}}} when {{{P=200}}} and {{{r=0.1}}}