$(10$ points$)$ You just turned $22$ years old, received your bachelor's degree, and accepted your

first job $($well done!$).$ Now you must decide how much money to put into your retirement plan.

The plan works as follows: Every dollar in the plan earns $7\%$ per year $($nominal rate of return$).$

You cannot make withdrawals until you retire on your ${65}^{th}$ birthday. After that, you can make

withdrawals as you see fit. You decide that you will plan to live to $100$ and work until you turn

You estimate inflation will be $3\%$ per year. To live comfortably in retirement, you will need

$$100,000$ per year $($real dollars$),$ starting at the end of the first year of retirement and ending on

your ${100}^{th}$ birthday. You will contribute the same amount to the plan at the end of every year

that you work.

a$.$ How much do you need to contribute each year to fund your retirement $($real dollars$)?$

b$.$ Stretch Problem: What is the age $65$ amount that you have calculated in real dollars

worth in terms of nominal dollars?

Hint: Use the formula below where 'Nominal $$\text{'}$ is nominal dollars at time$=$t$,$ 'Real $$\text{'}$ is

real dollars at time $=t,$ 'Infl' is inflation rate, and $\text{'}N\text{'}$ is the number of years of inflation.

Nominal $$=$ Real $${?}^{**}(1+$Inf${)}^N$