1. Fixed Contribution. If you contribute $250 per month to an Individual Retirement Account (IRA) for 40 years at an interest rate of 8% per year compounded continuously, how much money will be in your IRA at retirement?

2. Increasing Contribution. Usually, contributions are a percentage of your salary, which increases over time. Consider a $250 per month contribution, increased by 5% per year for 40 years at the same 8% rate, compounded continuously. In this case, how much money will be in your IRA at retirement? Note: R(t) will no longer be constant in this case it will depend on t. Your first step here is to figure out what R(t) is. Remember, to increase a number by 5%, you can multiply it by 1.05.

3. Making it last in retirement: Use your answer from question number 2 in this part. Let us suppose that you invest this amount in a secure investment earning a fixed interest rate of 6% per year, compounded continuously. If you want your nest egg to last for exactly 25 years, then what constant monthly payment should you draw off?