Two business partners have a bank balance of $17,942.00. After the first year their interest brings their balance to $18,928.91. What rate of interest is earned?

To find the rate of interest earned, we can use the formula for simple interest:

I = P \cdot r \cdot t

Where:
- I is the interest earned,
- P is the principal (initial balance),
- r is the interest rate, and
- t is the time in years.

In this problem, we are given the principal (\$17,942.00) and the final balance after one year (\$18,928.91).

Substituting these values into the formula, we have:

18,928.91 - 17,942.00 = 17,942.00 \cdot r \cdot 1

Simplifying the equation:

986.91 = 17,942.00 \cdot r

To find the rate of interest (r), we can divide both sides of the equation by the principal (\$17,942.00):

\frac{986.91}{17,942.00} = r

Calculating this expression:

r \approx 0.055 = 5.5\%

Answer: The rate of interest earned is approximately 5.5%.