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What is joe's first payment amount at the end of each year?

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Joe Hokie is a new client and wants you to help him figure out how much he should be saving for retirement. Joe just turned 22 years old today and said he wants to retire in 40 years when he turns 62 years old. He thinks that $40,000 a year in today's dollars will be enough for him to live on during retirement (including any taxes he might have to pay). After discussing risk and return with him, you both agree that he should be able to get a 10% annual return prior to retirement and a 6% annual return during retirement. You have also discussed inflation with Joe and he is comfortable with an assumed inflation rate of 4%. Based on his health and his family history, Joe believes he will die on his 80th birthday (Happy Birthday, Joe!). He also thinks that it makes sense to withdraw his retirement income at the beginning of each year and to increase his withdrawals each year in order to keep pace with inflation. Joe wants to deposit his savings in his company's 401k plan at the end of each year and wants to increase his annual payments by inflation as well. Joe wants to know what his first payment amount

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