Since the zero-coupon bond is compounded continuously, the future value of this 7-year, 9% per annum bond is calculated using the continuous compounding formula:

$\text{FV} = \text{Face value} \times e^{\text{rate} \times \text{period}}$ $= 1000 \times e^{0.09 \times 7}$ $= 1000 \times e^{0.63}$ $= 1000 \times 1.8776$ $= 1,877.6$

The formula for continuous compounding is $FV = PV \cdot e^{rt}$, where $e$ is the mathematical constant approximately equal to 2.71828, $r$ is the continuously compounded rate, and $t$ is the time period in years. Applying this to the zero-coupon bond gives a future value of $1,877.6, which matches option C.