## Calculus (3rd Edition)

(a) $1.0508$ (b) $1.0513$
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: $$e^{r}=e^{0.05} \approx 1.0513$$