Enrolment at the local university increased 20% over a four-year period. Determine the average annual rate of enrolment during this time.

A) 3.85%
B) 4.66%
C) 5.85%
D) 6.44%
E) 8.04%

The average annual rate of enrolment can be calculated using the formula for compound interest: $A=P(1+r{)}^n$ , where $A$ is the final amount, $P$ is the principal amount (initial amount), $r$ is the annual rate of increase, and $n$ is the number of years. Here, $A/P=1.20$ (since there's a 20% increase over the initial amount), and $n=4$ years. Rearranging the formula to solve for $r$ , we get $1.20=(1+r{)}^4$ . Taking the fourth root of both sides gives $1+r=\sqrt[4]{1.20}$ , which leads to $r\approx 0.0466$ or $4.66$ .