$4-22$ As a financial consultant, you are helping a client who just won a fortune in Las Vegas. The two of you are planning her retirement. She will make a deposit today $(1$ January $1991)$ in a time deposit that pays $8$ percent interest, compounded annually. She will retire in $25$ years $($on $1$ January $2016),$ and she expecus to live for another $30$ years $($until $31$ December $2045).$ Her husband is expected to live an additional five years $($until $31$ December $2050).$ She wants an income of $$30,000$ per year during her retirement years, the first payment to be received on $1$ January $2016$ and the last on $1$ January $2045.$ Further, ahe wans her husband to have an income of $$20,000$ after she is dead, or $$20,000$ on every $1$ January from $2046$ through $2050.$ Finally, she plans to take a trip to Satum in $2021$ and be gone for two years, so she wants to receive $$60,000$ on $1$ January $2021$ and nothing on $1$ January $2022.$

$2.$ How much must he deposit on $1$ January $1991$ in order to attain her retirement goal? $($Hint: Use a time line.$)$

b$.$ In terms of current dollars, how much will her $$30,000$ of income in $2016$ be worth in $1991$ dollars if we experience a constant $10$ percent inflation rate?