Suppose you are 35 years old and want to save for your retirement. You have two options, a bond fund and a stock fund. You decide to put money in both of them. Starting immediately, you will deposit $5,000 into each account (so the total is $10,000 right now). The amount you deposit into each account will increase by 4% each year after that initial deposit; you make the new deposit each year after your account has been credited for its return that year. You expect the bond account to earn 3% per year and the stock account to earn 5% per year. You do this for 20 years, at which time you are 55. At that point, you merge both accounts into one account whose risk is smaller. This account in mostly in Treasury securities and will earn 2% per year.
You continue to contribute the total amounts you would have contributed to the separate bond and stock funds. Ten years later, at age 65, you retire, stop making payments into the account, and begin to take payouts from this account to fund your retirement. If you want the payouts to last 20 years, how much can you take out each year?'