Given that Danielle deposits $200 into a bank account that compounds interest at a monthly rate of 1%;
[tex]\begin{gathered} \text{ Principal P = \$200} \\ \text{rate r = 1\% }=0.01 \\ \text{ number of times compounded per year }=12 \end{gathered}[/tex]If Danielle leaves her money in the bank for 5 years;
[tex]\text{time t }=5\text{ years}[/tex]Recall that the formula for compound interest is;
[tex]F=P(1+\frac{r}{n})^{nt}[/tex]where F is the final value;
[tex]\begin{gathered} F=P(1+\frac{r}{n})^{nt} \\ F=200(1+\frac{0.01}{12})^{12(5)} \\ F=200(1.000833333\ldots)^{60} \\ F=200(1.051249) \\ F=\text{ \$210.25} \end{gathered}[/tex]Therefore, the amount she will have is;
[tex]\text{ \$210.25}[/tex]