Step 1 :Given that the principal amount (P) is $318,000, the annual interest rate (r) is 5% or 0.05 in decimal, the number of times that interest is compounded per year (n) is 12 (since it's compounded monthly), and the time the money is invested for in years (t) is 11.
Step 2 :We use the compound interest formula A = P(1 + r/n)^(nt) to find the amount of money accumulated after n years, including interest.
Step 3 :Substituting the given values into the formula, we get A = 318000(1 + 0.05/12)^(12*11) = 550545.0141559908.
Step 4 :To find the amount of interest earned, we subtract the initial principal from the compound amount. So, the interest earned is 550545.0141559908 - 318000 = 232545.0141559908.
Step 5 :Rounding to the nearest cent, the compound amount after 11 years is \(\boxed{\$550545.01}\) and the amount of interest earned is \(\boxed{\$232545.01}\).