Answer
a) $\$ 1146.16$, $\$ 1143.39$ and $\$ 1148.69$
b) From best to worst, we have A, B, C.
Work Step by Step
a) The balance of the investments after the first two years are:
$$
\begin{gathered}
P=875\left(1+\frac{0.135}{365}\right)^{365(2)}=\$ 1146.16 \\
P=1000\left(e^{0.067(2)}\right)=\$ 1143.39 \\
P=1050\left(1+\frac{0.045}{12}\right)^{12(2)}=\$ 1148.69
\end{gathered}
$$
b) Compute and compare the rate of return.
$$
\begin{gathered}
P=875\left(1+\frac{0.135}{365}\right)^{365t}=875 \cdot(1.1445)^t \\
P=1000\left(e^{0.067t}\right)=1000\left(1.0693\right)^t \\
P=1050\left(1+\frac{0.045}{12}\right)^{12t}=1050 \cdot 1.04593^t
\end{gathered}
$$
Comparing the effective annual rates for each account, we see that investment A has the best annual yield per year than the other two.
From best to worst, we have A, B, C.
