Financial math

You plan to save for retirement by making annual deposits into a savings account.

There will be two time periods, one after the other, one for savings and one for withdrawals as follows:

Period 1, from time 1 through time 30, annual deposits

Period 2, from time 31 through time 60, annual withdrawals

The deposits will be put into a stock fund, with an expected annual growth rate of 11%. Inflation is expected to be 2.8% per year throughout the two time periods.

You wish the annual withdrawals to be equivalent to $40,000 (each year), in today's purchasing power.

Question 1: Determine a savings plan that will enable you to achieve this, such that the last withdrawal leaves a zero account balance. You may work either in constant dollars or actual dollars, or both; be sure to specify which you are using. Use smooth patterns for the savings deposits (uniform, linear gradient, or geometric gradient). You may use either formulas or a spreadsheet. If you use formulas, you might be able to enter the answer in the answer field. You may use tables with approximate interest rates. Or, you may send the spreadsheet.