Problem $3$:

Suppose today is the first day at your new job, which you plan to stick with until you retire in $18$ years. You currently have $$110,000$ in the retirement plan from your former employer that you plan to put into the retirement plan of the new employer $($i$.$e$.$ roll over your benefits$).$ You also plan to contribute $$12,000$ at the beginning of each year into your new employer's plan, which earns an average annual return of $6\%.$

Required: Provide an answer to the following. Round all final calculations to two decimal places. If needed, you can access the interest tables here. $($a$)$: How much should you expect to have when you retire in $18$ years?

$($b$)$: What is the expected annual interest rate earned during retirement if you make withdrawals of $$94,670$ at the end of each year for $20$ years during retirement?