When Zeke was $16$ years old, he got an after school job at this parent$$s

restaurant. His parents told him that if he put some of his earnings into an

IRA, they would contribute an equal amount to his IRA. That year, and

every year thereafter, Zeke deposited $$600$ into his IRA. When Zeke reached

$21$ years old, his parents stopped contributing, but Zeke increased his annual

deposit to $$1200$ and continued to deposit that amount annually until he

retired at age $65.$ His IRA paid

$6\%$

interest. Determine the following:

a$)$ The future value of the account.

b$)$ Zeke$$s total contributions and his parents$$ total contributions to the account.

c$)$ The total interest.

d$)$ The future value of the account if Zeke waited until he was $18$ before he

started the IRA.

e$)$ The future value of the account if Zeke waited until he was $25$ before he

started the IRA.