Matt plans to fund his individual retirement account with the maximum contribution of $$4000$ at the end of each year for the next $20$ years. If Matt can earn $6\%$ on his contributions, how much $($to the nearest dollar$)$ will he have at the end of the $20$th year?

Select one:

a$.$ $$102,829$

b$.$ $$120,000$

c$.$ $$155,971$

d$.$ $$103,472$

e$.$ $$147,142$