Question $2-$ Retirement Saving for Jenny

Jenny is considering opening an IRA in preparation for her retirement. She plans to save $$8,000$

per year with the first investment made one year from now. Her retirement account earns $6\%$ per

year on her investments and she plans to retire in $30$ years, immediately after making the last

$$8,000$ investment.

a$.$ How much will she have in her retirement account on the day of her retirement?

b$.$ If she hopes to live for $30$ years in retirement, how much can she withdraw every year in

retirement $($starting one year after retirement$)$ so that she will just exhaust her savings with

the ${30}^{th}$ withdrawal? Assume that her savings will continue to earn $6\%$ in retirement.

c$.$ If$,$ instead, she decides to withdraw $$60,000$ per year in retirement $($again with the first

withdrawal one year after retiring$),$ how many years will it take until she exhausts her savings?

Assume that her savings will continue to earn $6\%$ in retirement.

d$.$ If she hopes to retire having $$1,000,000$ saved in her retirement account, what is the

minimum annual return that her retirement account must earn for the next $30$ years? Assume

that she keeps saving $$8,000$ per year with the first investment made one year from now.