Answer
a. $A_1=10000(1+\frac{0.05}{4})^{4t}$. $A_2=10000(1+\frac{0.045}{12})^{12t}$.
b. the $5\%$ account (red curve).
Work Step by Step
a. For the $5\%$ account, we have $r=0.05, n=4$ and $A_1=10000(1+\frac{0.05}{4})^{4t}$. For the $4.5\%$ account, we have $r=0.045, n=12$ and $A_2=10000(1+\frac{0.045}{12})^{12t}$.
b. Graph both functions; we can see that the $5\%$ account (red curve) rises faster and thus offers a better return.
