The following are the timing assumptions for your retirement planning:
-you will save with annual payments into a retirement savings account
-your first payment will be made on your 23rd birthday (thus, there will be zero interest earned during your 23rd year (while you are age 22))
-your last payment will be made on your 65th birthday
-your annual payment will be constant through time
-you will retire from work on your 65th birthday, the day of your last payment
-you will withdraw from your retirement savings your first retirement withdrawal on your 65th birthday (given this assumption and the previous, it is as if your savings deposits are made via automatic payroll deduction. But on your 65th birthday you retire, so no more paychecks are forthcoming. You need to make your first withdrawal that day in order to fund your living expenses over the next year.)
The following are the investment and consumption assumptions for your retirement planning:
-your investments will earn a (geometric) average return of 8% per year during your pre-retirement years
-your investments will earn a (geometric) average return of 2% per year during your retirement years
-you will withdrawal a constant $100,000 per year from your retirement savings, beginning on your 65th birthday through your 84th birthday (the withdrawal on your 84th birthday will fund your living expenses during your 85th birthday, and it will leave you with a zero balance)
Solve for the annual savings amount necessary to fund this retirement plan.