For the next $19$ years, the Patricks will receive a $$16000$ check at the end of

every year as part of an insurance settlement.

a$.$ Assuming they were to deposit that money into an account at $4\mathrm{.}6\%$

compounded continuously, how much would their account be worth at

the end of the $19$ years? $($Round your answer to the nearest dollar.$)$

b$.$ The Patricks are offered a one$-$time lump sum amount payment, the

amount being what they would need now that would grow to the

future value found in Part $($a$)$ at the same percentage rate. What is that

lump sum? $($Round your answer to the nearest dollar.$)$