Answer
There will be around $504$ rats by next January.
Work Step by Step
This involves exponential growth as the population will increase by 2.5 percent annually.
RECALL:
Exponential growth is represented by the formula
$y=C(1+r)^x$
where
C = initial/original amount
r = growth rate
x = number of time intervals
The given situation has:
C = 200
r = $8\%$ per month
x = 12 months
Substitute these values into the given formula above to have:
$y=200(1+8\%)^{12}
\\y=200(1+0.08)^{12}
\\y=200(1.08^{12})
\\y \approx 504$
