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%

Question

Quizplus · Accepted Answer

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 $4.66%$.

Enrolment at the Local University Increased 20% Over a Four-Year