You will almost certainly be a millionaire by the time you retire in $50$ years. Bad news: The inflation rate over your lifetime will average about $3\%.$

a$.$ What will the real value of $$1$ million be by the time you retire in terms of today$$s dollars?

b$.$ What real annuity $($in today$$s dollars$)$ will $$1$ million support if the real interest rate at retirement is $2$ percent and the annuity must last for $20$ years.