• Bill and Bob are both 35 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 10%. Both plan on retiring at age 60, 25 years from today, and both want to have $2 million saved by age 60. 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 26 total contributions (t = 0, 1, 2, ... 25), while Bob plans to make 25 total contributions (t = 1, 2, ... 25). How much more than Bill will Bob need to save each year in order to accumulate the same amount as Bill does by age 60?
• Today you opened up a local bank account. Your plan is to make five $4,000 contributions to this account. The first $4,000 contribution will occur today and then every six months you will contribute another $4,000 to the account. (So your final $4,000 contribution will be made two years from today). The bank account pays a 6% APR that is compounded monthly. After two years, you plan to leave the money in the account earning interest, but you will not make any further contributions to the account. How much will you have in the account 6 years from today?