You are currently 30 years of age. You intend to retire at age 60 and you want to be able to receive a 20-year, $100,000 beginning-of-year annuity with the first payment to be received on your 60th birthday. You would like to save enough money over the next 15 years to achieve your objective; that is, you want to accumulate the necessary funds by your 45th birthday.

a. If you expect your investments to earn 12 percent per year over the next 15 years and 10 percent per year thereafter, how much must you accumulate by the time you reach age 45?

b. What equal, annual amount must you save at the end of each of the next 15 years to achieve your objective, assuming that you currently have $10,000 available to meet your goal? Assume the conditions stated in Part a.