Suppose you are doing some investment planning. Your goal is to have enough money when you retire so that you can take out $50,000 per year for 30 years. You are planning on building up this money by making monthly deposits to an investment account over the next 40 years.
(a) If you expect that in retirement your account will earn 5%, how much will you need to generate the payments that you want?
(b) If you expect that while you are saving your investment account will earn 10% (the rate is higher during this time because you are assuming you will take on higher risk but higher reward investments than you will when you are retired), how much should you deposit each month?
Show your work.