Joey is terminally ill and expects to live $5$ years. His wife will need $$16,000\mathrm{.}00$ in addition to her income at the beginning of each year for $4$ years beginning at the time of his death to pay off their debt in $4$ years. Assume $6\mathrm{.}8\%$ interest compounded annually is earned on Joey$$s account.

a$.$ Calculate the amount that must be in the account at the time of his death to satisfy this need.

b$.$ Calculate the total amount of interest earned on the account during the $4$ years.