Suppose you are planning for retirement. At the beginning of this year and each of the next 39 years, you plan to contribute some money to your retirement fund. Each year, you plan to increase your retirement contribution by $500. When you retire in 40 years, you plan to withdraw $100,000 at the beginning of each year for the next 20 years. You assume the following about the yields of your retirement investment portfolio:

■ During the first 20 years, your investments will earn 10% per year.

■ During all other years, your investments will earn 5% per year.

All contributions and withdrawals occur at the beginnings of the respective years.

a. Given these assumptions, what is the least amount of money you can contribute this year and still have enough to make your retirement withdrawals?

b. How does your answer change if inflation is 2% per year and your goal is to withdraw $100,000 per year (in today’s dollars) for 20 years?