To calculate the interest earned on a savings account with compound interest, we use the formula A = P(1 + r/n)^(nt). Here, A is the final amount, P is the principal amount ($500.00), r is the annual interest rate (9% or 0.09), n is the number of times interest is compounded per year (quarterly, so n = 4), and t is the number of years the money is invested (9 years). Plugging in the values: A = 500(1 + 0.09/4)^(4*9). This simplifies to A = 500(1 + 0.0225)^(36) = 500(1.0225)^(36). Calculating this gives A ≈ 1113.91. The interest earned is then A - P = 1113.91 - 500 = 613.91. Therefore, Savannah will earn $613.91 in interest after 9 years.