Problem $6\mathrm{.}1$: You recently graduated from college and started your first full$-$time job. You are going to take your parent's advice and start saving early for your retirement.

a$)$ If you invest $$4,000$ at the end of each year into a Roth IRA for the next $45$ years and earn $8\%$ compounded annually, how much will you have when you retire in $45$ years? What would the figure be if your Roth IRA only earned $6\%$ compounded annually?

b$)$ What if you didn't get serious about your retirement savings for the first $5$ years you worked and thus you invested $$4,000$ each year in the Roth IRA for only $40$ years? How much would the Roth IRA account grow at both the $8\%$ and $6\%$ figures used in part $\text{'}$a$\text{'}?$

Hint: see example problem on pages $160-163$

a$)$

$\backslash$table$[[$PV$,],[i,],[n,],[$pmt$,],[$FV$,]]$

b$)$

$\backslash$table$[[$PV$,],[i,],[n,],[pmt,],[FV,]]$