Assume that your brother is now $50$ years old, that he plans to retire in $10$ years, and that he expects to live for $25$ years after he retires $($i$.$e$.$ until he is $85$ years

old$).$ He wants a fixed retirement income that has the same purchasing power at the time he retires as $$50,000$ has today $($he realizes that the real value of his

retirement income will decline year by year after he retires$).$

His retirement income will begin pm the day he retires, $10$ years from today, and he will then get $24$ additional annual payments.

Inflation is expected to be $3\%$ per year from today forward. Your brother currently has a savings of $$275,000$ and expects to earn a return on his savings of $8\%$ per

year, annual compounding.

To the nearest dollar, how much must your brother save during each of the next $10$ years $($with deposits being made at the end of each year$)$ in order to meet his

retirement goal?