Raymond Farringdon was thing that her would like to expects to retire in $15$ years and has suddenly realized that he hasn't saved anything toward that goal. After giving the matter some thought, he has decided that he would like to retire with enough money in savings to withdraw $$85,000$ per year for $25$ years after he retires. Assume a $6\%$ return on investment before and after retirement and that all payments into and withdrawals from savings are at year end.

a$.$ How much does Raymond have to save in each year for the next $15$ years to reach this goal?

b$.$ How much would Raymond have needed to save each year if he had started when retirement was $25$ years away?

c$.$ Comment on the difference between the results of parts a and

b$.(10$ points$)$