Answer
$r=0.08 $; it is better to receive $\$ 1000$ today
$r=0.03$; it is better to receive $\$ 1300$ after $4$ years
Work Step by Step
Since $r= 0.08$, then for $t=4$ years and $P= \$ 1300$, we have
\begin{align*}
P V&=P e^{-r t}\\
&=1300 e^{-0.08 (4)} \\
&\approx 943.99
\end{align*}
Hence, it is better to receive $\$ 1000$ today.
For $ r=0.03 $, $t=4$ years, and $P= \$ 1300$, we have
\begin{align*}
P V&=P e^{-r t}\\
&=1000 e^{-0.03 (4)} \\
&\approx 1152..99
\end{align*}
Hence, it is better to receive $\$ 1300$ in $4$ years.
