You$$ve just started a new job and the human resource director has presented you with two different retirement investment options. With option $1,$ you will have $$7,300$ automatically taken out of your paycheck annually and are projected to receive an interest rate of $7\mathrm{.}75\%$ compounded annually. The second retirement option has a contribution expectation of only $$5,600$ annually, but the interest rate is $10\mathrm{.}5\%$ and is compounded annually. In either case, you expect to work and contribute to your retirement in this same fashion for the next $33$ years.

a$)$ Which retirement option gives you more purchasing power once you retire?

b$)$ What other important financial factors might you ask your human resource director regarding your retirement $($hint: there are a number of important factors to consider with such a long investment$)?$ Briefly $(1-2$ sentences for each$)$ discuss two of the factors you would consider.