$1.$ Assume you can earn $8\%$ on your retirement savings. What would be the annual contribution required in order to achieve a retirement nest egg of $$1,000,000$ at the age of $65$ if you begin your savings at the age of $25.$

Enter your answer as a positive number without commas or dollar signs. Round up or down to the nearest penny.

$2.$ It is your first day of work and you are enrolling in the company sponsored $401($k$)$ plan. The company has a generous match policy; dollar$-$for$-$dollar up to $4\%$ of salary. $4\%$ of your salary is $$1,200.$ Looking at the funds you choose for investments in the plan, it's fair to assume an $8\%$ before tax annual return and you assume $45$ years until retirement.

a$.$ How much will you have in your $401($k$)$ plan upon retirement?

Assume one annual contribution at the end of every year. Enter your answer as a positive number without commas or dollar signs. Round up or down to the nearest penny.

b$.$ If you believe you will continue to earn $8\%$ on your investments during retirement and you assume you are funding a $20$ year retirement, how much will you be able to spend annually in retirement on an after$-$tax basis assuming a $20\%$ federal tax rate?

Enter your answer as a positive number without commas or dollar signs. Round up or down to the nearest penny.