We have that the compound interest continuously is given by the formula:
[tex]A=Pe^{rt}[/tex]Where:
A = Future value
P = Initial value = 1000
r = rate = 0.0775
t = 1 year
Substitute the values:
[tex]A=1000e^{0.0775(1)}=1000e^{0.0775}=1080.58[/tex]Answer: $1080.58