a$.$ Suppose that between the ages of $22$ and $26,$ you contribute $$$$9000$ per year to a$401($k$)$ and your employer contributes $$4500$per year on your behalf. The interest rate is$7\mathrm{.}7\%$ compounded annually. What is the value of the$401($k$)$ after $4$ years?$$b$.$ Suppose that after $4$ years of working for this$$ firm, you move on to a new job.$$ However, you keep your accumulated retirement funds in the$401($k$).$ How much money will you have in the plan when you reach age$65?$c$.$ What is the difference between the amount of money you will have accumulated in the$401($k$)$ and the amount you contributed to the$$ plan?$$