Question 189665
a)



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



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



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



{{{P+Pr+P(r^2/4))}}} Distribute



{{{P(r^2/4)+Pr+P}}} Rearrange the terms.



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b)



There are two ways to do this:


Method #1:



{{{P(1 + r/2)^2}}} Start with the original expression



{{{200(1 + 0.1/2)^2}}} Plug in {{{P=200}}} and {{{r=0.1}}}



{{{200(1 + 0.05)^2}}} Divide



{{{200(1.05)^2}}} Combine like terms.



{{{200(1.1025)}}} Square 1.05 to get 1.1025



{{{220.5}}} Multiply



So after a year, we have $220.50 in the account


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Method #2:



{{{P(r^2/4)+Pr+P}}} Start with the expanded polynomial (from part a)




{{{200(0.1^2/4)+200(0.1)+200}}} Plug in {{{P=200}}} and {{{r=0.1}}}



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



{{{200(0.0025)+200(0.1)+200}}} Divide



{{{0.5+20+200}}} Multiply



{{{220.5}}} Combine like terms.




So using either method, we get $220.5