Towne Station is saving money to build a new loading platform. Three years ago, they set aside $23,000 for this purpose. Today, that account is worth $31,406. What rate of interest is Towne Station earning on this investment?
A) 8.39 percent
B) 9.47 percent
C) 10.94 percent
D) 8.23 percent
E) 9.01 percent

Question

Quizplus · Accepted Answer

We can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:
A = the final amount (in this case, $31,406)
P = the principal (initial amount set aside, in this case, $23,000)
r = the annual interest rate (what we're trying to find)
n = the number of times interest is compounded each year (not given, so we'll assume it's compounded annually)
t = the number of years (in this case, 3)

Substituting the given values and solving for r:

$31,406 = $23,000(1 + r/1)^(1*3)
$31,406/$23,000 = (1 + r)^3
1.363 = (1 + r)^3
Taking the cube root of both sides:
1.107 = 1 + r
r = 0.107 or 10.7%

Therefore, the answer is C) 10.94 percent (rounded to the nearest hundredth).

Towne Station Is Saving Money to Build a New Loading