1. You are planning on retiring in forty-five years and wish to have $3,000,000 at that time. You will make your first payment in one year and then increase your payments by 2.25 percent annually thereafter. If you invest in a fund paying an annual percentage rate (APR) of ten percent, compounded semiannually, what is the amount of the first payment necessary to reach your objective.
2. You have just retired and reached your objective (see above) of accumulating $3,000,000 in your retirement fund. You expect to live for another twenty-five years (exactly) and wish to leave $1,500,000 to Illinois Tech when you are gone. What is the most that you could withdraw from this fund at the end of each quarter and still leave the money to IIT? The fund is expected to return nine percent per annum, compounded monthly?