If the payments made to Mr. Potts (or his descendants) is a perpetuity of $120,000 annually beginning one year after Andrew's retirement, how much would Garcia Energy need at the beginning of the distribution period.Assume that the applicable interest rates are 9 percent and 6 percent, during the accumulation and distribution period, respectively. Report:

a. Size of the amount available when Mr. Potts retires.

b. Size of the "accumulation period" end-of-year annuity needed

The long-run goal of many is enjoying a long, gratifying retirement without financial worries. This is the case for Andrew Potts. He is attempting to manage Garcia Energy in such a way that it provides for his retirement through the accumulation of funds during his working years.Mr. Potts is expecting to retire in 20 years, at the age of 70. Upon retirement, he is seeking an annual beginning-of-the year payment of $120,000 for 16 years. For ease of computation, assume that if Andrew dies prior to the end of the 16-year period, annual payments will pass to his wife and/or heirs.

During the 20-year "accumulation period" Garcia Energy wishes to fund the annuity by making equal, annual, end-of-year deposits into a mutual fund historically earning 8% interest. Once the 16-year "disbursement period" begins, Garcia Energy plans to move the accumulated monies into an account earning a guaranteed 4% per year. At the end of the distribution period, the account balance will be zero.Note that the first deposit will be made at the end of Year 1 and that the first distribution payment will be received at the end of Year 20 (which is the beginning of year 21)