Question 152830
Let's start with the first part of the question, which is rewriting the expression without parentheses.
{{{P(1+ r/2)^2}}}
{{{P(1 + r/2)(1 + r/2)}}}
We can use the FOIL method. (Multiply the pairs: front, outside, inside, then last)
{{{P(1 + r/2 + r/2 + (r^2)/2)}}}
{{{P(1 + r + (r^2)/4)}}}
{{{P + Pr + (Pr^2)/4)}}}
<br>Now we can evaluate this new expression by plugging in P = $200 and r = 0.1 (10% equals 10/100 or 1/10):
{{{P + Pr + (Pr^2)/4)}}}
{{{200 + 200(0.1) + 200(0.1)^2/4}}}
{{{200 + 20 + 200*0.01/4)}}}
{{{220 + 2/4)}}}
{{{220 + 1/2)}}}
{{{220.5}}}
<br>Therefore, the value of the investment after one year is $220.50.