How much must you deposit each year into your retirement account starting now and continuing through year $9,$ if you want to be able to withdraw

$$80,000$ per year forever, beginning $30$years from

now? Assume the account earns interest at $($a$)$ the

generous rate of $10\%$ per year, and $($b$)$ a more conservative rate of $4\%$ per year. Compare the two amounts.