Solution:
The compound interest formula is
[tex]\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ A\text{ is the amount} \\ P\text{ is the principal} \\ r\text{ is the interest rate} \\ t\text{ is the time in years} \end{gathered}[/tex]If you sign up for an account now, you get 2 years of 12% annual interest rate compounded monthly, i.e.
[tex]\begin{gathered} t=2\text{ years } \\ R=12\% \\ r=\frac{R}{100}=\frac{12}{100}=0.12 \\ n=12\text{ \lparen compounded monthly\rparen} \\ P=\text{\$200} \end{gathered}[/tex]The amount after the first two years is
[tex]\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ A=200(1+\frac{0.12}{12})^{12\times2} \\ A=200(1+0.01)^{24} \\ A=200(1.01)^{24} \\ A=\text{\$253.95} \end{gathered}[/tex]The amount after the first two years is $253.95 (nearest cent)
For the rest of the time, i.e. the next 2 years,
Where
[tex]\begin{gathered} P=\text{\$253.95} \\ R=8\% \\ r=\frac{R}{100}=\frac{8}{100}=0.08 \\ n=12\text{ \lparen compounded monthly\rparen} \\ t=2\text{ years} \end{gathered}[/tex]The amount for after 4 years will be
[tex]\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ A=253.95(1+\frac{0.08}{12})^{12\times2} \\ A=\text{\$297.85 \lparen nearest cent\rparen} \end{gathered}[/tex]Hence, the amount after 4 years is $297.85 (nearest cent)
