For the next $14$ years, Debra will receive a $$14000$ check at the end of every year as part of an insurance settlement. $($Round your answers to the nearest dollar. Only round your final answers. Do not round intermediate steps.$)$

a$.$ Assuming she were to deposit that money into an annuity at $4\%$ compounded continuously, how much would her annuity be worth at the end of the $14$ years?

b$.$ She is offered a one$-$time lump sum amount payment, the amount being what she would need now that would grow to the future value found in part $($a$)$ at the same percentage rate. What is that lump sum?