James Industries wishes to accumulate funds to provide a retirement annuity for its vice president of research, Jesse Morgan. Ms. Morgan, by contract, will retire at the end of exactly 12 years. Upon retirement, she is entitled to receive an annual end-of- year payment of $42,000 for exactly 20 years. If she dies prior to the end of the 20- year period, the annual payments will pass to her heirs. During the 12-year accumulation period, James wishes to fund the annuity by making equal, annual, end- of-year deposits into an account earning 9% interest. Once the 20-year distribution period begins, James plans to move the accumulated monies into an account earning a guaranteed 12% per year. At the end of the distribution period, the account balance will equal 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 13. To Do a. Draw a time line depicting all of the cash flows associated with James's view of the etirement annuity. b. How large a sum must James accumulate by the end of year 12 to provide the 20- year, $42,000 annuity? c. How large must James's equal, annual, end-of-year deposits into the account be over the 12-year accumulation period to fund fully Ms. Morgan's retirement annuity? d. How much would James have to deposit annually during the accumulation period if it could earn 10% rather than 9% during the accumulation period? e. How much would James have to deposit annually during the accumulation period if Ms. Morgan's retirement annuity were perpetuity and all other terms were the same as initially described? James Industries wishes to accumulate funds to provide a retirement annuity for its vice president of research, Jesse Morgan. Ms. Morgan, by contract, will retire at the end of exactly 12 years. Upon retirement, she is entitled to receive an annual end-of- year payment of $42,000 for exactly 20 years. If she dies prior to the end of the 20- year period, the annual payments will pass to her heirs. During the 12-year accumulation period, James wishes to fund the annuity by making equal, annual, end- of-year deposits into an account earning 9% interest. Once the 20-year distribution period begins, James plans to move the accumulated monies into an account earning a guaranteed 12% per year. At the end of the distribution period, the account balance will equal 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 13. To Do a. Draw a time line depicting all of the cash flows associated with James's view of the etirement annuity. b. How large a sum must James accumulate by the end of year 12 to provide the 20- year, $42,000 annuity? c. How large must James's equal, annual, end-of-year deposits into the account be over the 12-year accumulation period to fund fully Ms. Morgan's retirement annuity? d. How much would James have to deposit annually during the accumulation period if it could earn 10% rather than 9% during the accumulation period? e. How much would James have to deposit annually during the accumulation period if Ms. Morgan's retirement annuity were perpetuity and all other terms were the same as initially described