Answer
False.
Replace "will increase without bound" with "will not increase without bound" or with "will approach the amount obtained by continuous compounding."
Work Step by Step
The model for n compounding periods per year is $ A=P(1+\displaystyle \frac{r}{n})^{nt}$
approaches, as the number n increases, the continuous model, by which $ A=Pe^{rt}.$
So, the statement is false.
