Alpha, Inc. is saving money to build a new factory. Six years ago they set aside $250,000 for this purpose. Today, that account is worth $306,958. What rate of interest is Alpha earning on this money?
A) 3.43%
B) 3.45%
C) 3.48%
D) 3.52%
E) 3.55%

Question

Quizplus · Accepted Answer

The interest rate can be found using the formula for compound interest: $A = P(1 + r)^n$, where $A$ is the amount of money accumulated after n years, including interest, $P$ is the principal amount, $r$ is the annual interest rate, and $n$ is the time the money is invested for in years. Rearranging the formula to solve for $r$, we get $r = \left(\frac{A}{P}\right)^{\frac{1}{n}} - 1$. Substituting the given values ($A = 306,958$, $P = 250,000$, $n = 6$) into the formula gives $r = \left(\frac{306,958}{250,000}\right)^{\frac{1}{6}} - 1 \approx 0.0348$ or 3.48%.