Since the money is deposited on an account that gets compounded monthly, we need to use the following expression:
[tex]A=P\cdot(1+\frac{r}{n})^{nt}[/tex]Where A is the final amount, P is the invested principal, r is the interest rate, n is the number of times it get compounded in a year, and t is the number of elapsed years.
[tex]\begin{gathered} A=300\cdot(1+\frac{0.1}{12})^{12\cdot3} \\ A=300\cdot(1+0.00833)^{36}_{} \\ A=300\cdot(1.00833)^{36} \\ A=300\cdot1.34802 \\ A=404.41 \end{gathered}[/tex]Erin will be able to spend $404.41 on the bike.