Twenty years ago, Max invested $$10,000.$ Thirty years ago, Julie invested $$5,000.$ Today, both Max and Julie's investments are each worth $$35,000.$ Which one of the following statements is correct concerning their investments? Assume that they will continue earning the same rate of return.

a$.$ Max has earned an average annual interest rate of $6\mathrm{.}41\%.$

b$.$ Max has earned more interest on interest than Julie.

c$.$ Julie has earned an average annual interest rate of $6\mathrm{.}7\%.$

d$.$ Two years from now, Max's investment will be worth more than Julie's.

e$.$ Last year, Julie's investment was worth more than Max's.