Mr$.$ Brown decided to sell his farm and to deposit the earnings into

an account. After calculating the interest at $5\mathrm{.}3\%$ p$.$a$.$ compounded

annually, he found that he can withdraw $$88,000$ at the end of each

year for $10$ years.

$($a$)$ If the withdrawals are deferred by $6$ years, then what is the

present value of his earnings? $($Give your answer rounded to

the nearest cent.$)$

$($b$)$ Suppose Mr$.$ Brown sold his farm for $$550,000.$ For how many

years are the withdrawals deferred? $($Give your answer rounded

to the nearest year.$)$