Step 1: Find the effective annual rate required:

Amount deposited today × (1 + Rate of interest) = Amount next year

Rate of interest = (Amount next year / Amount deposited) − 1 = ($5,500 / $5,040.11) − 1 = 0.0912 or 9.12% (effective annual rate)

Step 2: Convert the effective annual rate to a nominal rate compounded monthly using:

$`$1` + i = \left(1 + \frac{i_m}{m}\right)^m$$

$`$1.09`12 = \left(1 + \frac{i_{12}}{12}\right)^{12}$$

$i_{12} = \left[1.0912^{1/12} - 1\right] \times 12 = 0.08759 \approx 8.76\%$

Since the question asks for the annual interest rate compounded monthly, the answer is 8.76%.