Joe Smith has decided to start to save for retirement. He is $25$ years old and he expects to retire in $40$ years. He has calculated that if he were to retire today his annual living expenses would be $$65,000.$

He expects inflation to average $4\mathrm{.}0\%$ a year and that he will start withdrawing the money immediately the day he retires $($on an annual basis and adjusted for inflation each year after the initial withdrawal$).$

He expects to live until he is $90$ and his financial planner has offered him a product that will produce a $10\%$ annual return for pre and post retirement. He has decided to start contributing to his account today and he will make equal payments for the next $39$ years $($starting today and on an annual basis$).$

How much money does he need to put away each year to reach his goal? HINT: Use a real rate of return for your annuity in retirement.