Answer
(a) $ 1.0508$
(b) $ 1.0513 $
Work Step by Step
Since $$ r=0.05 $$
(a) The rate is compounded three times ($M=3 $), continuously, so we have
\begin{aligned}
P(t)&=P_{0}\left(1+\frac{r}{M}\right)^{M t}\\
&= \left(1+\frac{0.05}{3}\right)^{3} \\
&\approx 1.0508
\end{aligned}
(b) The rate is compounded continuously, so
\begin{aligned}
P&=P_{0} e^{r t}
\end{aligned}
Thus, the yearly multiplier is:
$$
e^{r}=e^{0.05} \approx 1.0513
$$
