I. Estimate Nest Egg:

Assuming a $3\%$ interest rate, use the Payout Annuity formula to determine your required nest egg $($amount needed at retirement$)$ to be able to withdraw $$\frac{2500}{?}$ month for $20$ years.

II$.$ Calculate Investment Requirements:

You have $40$ years until you can retire and have found an annuity paying $3\%$ per month. How much will you need to deposit each month for the next $40$ years to have your required nest egg $($part I above$)?$

III. Interest:

Determine the amount of your nest egg that is earned interest.