Bill and Bob are both 25 years old today. Each wants to begin saving for his retirement. Both plan on contributing a fixed amount each year into brokerage accounts that have annual returns of 12 percent. Both plan on retiring at age 65, 40 years from today, and both want to have $3 million saved by age 65. The only difference is that Bill wants to begin saving today, whereas Bob wants to begin saving one year from today. In other words, Bill plans to make 41 total contributions (t = 1, 2,.. 40).
How much more than Bill will Bob need to save each year in order to accumulate the same amount as Bill does by age 65?