A boy is now $11$ years old. On his fifth birthday he

received a gift of $$5,000$ from his grandparents, which

was invested in a $10$ year fixed deposit bearing an

interest rate of $6\%$ per year compounded annually. His

parents plan to have $$6,000$ available each year for the

boy$$s nineteenth to twenty second birthdays to help

finance his college education. To assist the financing, the

fixed deposit will be reinvested when it matures. If

required how much equal amount should the parents

deposit each year, beginning from his next birthday, so

that one year after the last deposit they can start making

payments to their son. All future investments will earn $6\mathrm{.}5\%$

per year compounded annually