You are $40$ years old and want to retire at age $60.$ Each$$ year, starting one year from$$ now, you will deposit an equal amount into a savings account that pays $7\%$ interest. The last deposit will be on your $60$th birthday. On your $60$th birthday you will switch the accumulated savings into a safer bank account that pays only $4\%$ interest. You will withdraw your annual income of $$$$140,000$ at the end of that year$($on your $$birthday$)$ and each subsequent year until your $85$th birthday. On that birthday you want to give $$$$1,000,000$ to your children. How much do you have to save each year to make this retirement plan$$ happen?