$1.$ Mr McDonald wants to start a college fund to pay for the studies of his daughter, who was born today. He has calculated that the studies will cost $20$k per year for $3$ years and the first amount has to be available on his daughter's $19$th birthday. He wants to fill the fund by paying an equal amount into the fund every year on his daughter's birthdays, the first payment today and the last one on her $18$th birthday. The interest rate is $2\%$ per year. How large must each of Mr McDonald payments be to fill the fund?