Consider the following game. You have a bank account that is compounded continuously [1] with an interest rate of . Your banker offers you the following deal. At any time in the future, you can pay dollars using only the interest from the account to increase your interest rate to . If your balance is at the time of the upgrade, then your balance will remain at for years, which is the time required to pay dollars from interest alone. After the years, the account grows with interest rate . Other than paying for the interest upgrade, you can never add or subtract any money until retirement, which is very far in the future. When should you accept the banker's offer? Let us call this game "the second banker's problem." For the first banker's problem, the balance is decreased by at the time of the purchase.