What is the nominal annual rate of interest compounded monthly at which $747.00 will accumulate to $1294.57 in eight years and eleven months? The nominal annual rate of interest is ?%. (Round the final answer to four decimal places as needed. Round all intermediate values to six decimal places as needed)

Step 1 ：We are given that the principal amount (P) is $747.00, the final amount (A) is $1294.57, the interest is compounded monthly (n = 12), and the time (t) is 8 years and 11 months which is approximately 8.9167 years. We need to find the annual interest rate (r).

Step 2 ：We can use the formula for compound interest, which is \(A = P(1 + r/n)^{nt}\), and rearrange it to solve for r: \(r = n[(A/P)^{1/nt} - 1]\).

Step 3 ：Substituting the given values into the formula, we get \(r = 12[(1294.57/747.00)^{1/(12*8.9167)} - 1]\).

Step 4 ：Solving the above equation, we get \(r = 0.06182624157667682\).

Step 5 ：This is the annual interest rate in decimal form. To convert it to a percentage, we multiply it by 100 and round to four decimal places, giving us \(r = 6.1826\%\).

Step 6 ：Final Answer: The nominal annual rate of interest compounded monthly at which $747.00 will accumulate to $1294.57 in eight years and eleven months is \(\boxed{6.1826\%}\).