The rule of the compounded interest is
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]A is the new amount
P is the initial amount
r is the interest rate in decimal
n is the number of periods per year
t is the number of years
Since the initial amount is $1100, then
P = 1100
Since the interest rate is 5.5%, then
[tex]r=\frac{5.5}{100}=0.055[/tex]r = 0.055
Since the interest is compounded monthly, then
n = 12
Since the time is 2 years, then
t = 2
Substitute them in the rule above to find A
[tex]\begin{gathered} A=1100(1+\frac{0.055}{12})^{12\times2} \\ A=1100(1+\frac{11}{2400})^{24} \\ A=1227.597324 \end{gathered}[/tex]Lydia's return after 2 years is $1227.60 to the nearest cent
