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 rate in decimal
n is the number of the periods per year
t is the time in years
Since the initial amount is $550, then
P = 550
Since the rate is 1.4%, then
r = 1.4/100 = 0.014
Since it is compounded monthly, then
n = 12
Since it is for 2 years, then
t = 2
Substitute them in the rule above to find A
[tex]\begin{gathered} A=550(1+\frac{0.014}{12})^{12\times2} \\ A=565.6083953 \end{gathered}[/tex]The total cost of Sylvie's loan is $565.61 to the nearest cent
