The value of an investment, in dollars, is modeled by the function $V(t)=P\cdot (1+r{)}^t$, where $P$ is the initial investment, $r$ is the annual growth rate, and $t$ is the number of years. If the investment is worth $1,200 after 2 years and $1,800 after 4 years, what was the initial investment $P$?