9. Vega Industries wishes to accumulate funds to provide a retirement annuity for its vice president of research, Mr. Abebreseh by contract will retire at the end of exactly 12 years. Upon retirement, he is entitled to receive an annual end-of-year payment of $45,000 for exactly 20 years. If he dies prior to the end of the 20-year period, the annual payments will pass to his heirs. During the 12-year accumulation period" Vega 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, Vega 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. Required a. Draw a time line depicting all of the cash flows associated with Vega's view of the retirement annuity. b. How large a sum must Vega accumulate by the end of year 12 to provide the 20-year, $45,000 annuity? c. How large must Vega's equal annual end-of-year deposits into the account be over the 12-year accumulation period to fund fully Mr. Abebreseh retirement annuity? d. How much would Vega have to deposit annually during the accumulation period if it could earn 10% rather than 9% during the accumulation period? e. How much would Vega have to deposit annually during the accumulation period if Mr. Abebreseh's retirement annuity were perpetuity and all other terms were the same as initially described