A) $205.03
The formula for calculating compounded interest is [tex]x=s(1+\frac{r}{n})^{nt}[/tex], where r is the rate of change (0.05), n is the number of times per year interest is compounded (4), s is the starting amount (200), and t is the number of years (0.5).
Substitute these values in to get [tex]x=200(1+\frac{0.05}{4})^{4*0.5}[/tex]. The fraction can be simplified further to get [tex]x=200(1.0125)^{4*0.5}[/tex].
Now simplify the multiplication in the exponent to get [tex]x=200(1.0125)^{2}[/tex]. Then solve the exponent. [tex]x=200(1.02515625)[/tex]
Finally, multiply. You end up with $205.03125, which can be rounded to $205.03.
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