Your grand aunt is planning to take a three$-$year leave of absence $($She will be living at austerity camp$)$ with no pay seven years from now. Your grand aunt will need $$20,000$ at the beginning of each of the three years for living expenses. Assume that interest rates will be $12\%$ compounded annually for the next twelve years. How much should your grand aunt deposit at the end of each year for the next seven years in order to pay for her leave?