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Finding Mr. Lauren Retirement Annuity

Sunrise Industries aims to collect funds to provide its research vice-president, Mr. Lauren, with a retirement annuity. Mr. Lauren will retire after precisely twelve years. Upon retirement, he will receive an annual end-of-year payment of $42,000 for exactly 20 years. If he dies before the 20-year period expires, annual payments will pass to his heirs. During the 12-year "accumulation period," Sunrise needs to fund the annuity by making equivalent annual end-of-year deposits into a 9-per-cent interest account. When the 20-year "distribution era" begins, Sunrise aims to transfer the accrued money into an account receiving a guaranteed 12% per annum. The account balance would equal zero at the end of the delivery cycle. Notice that the first Case Initial sum Annual cash flow rate deposit will be made at year 1 end and the first delivery payment will be issued at year 13 end.

Required

a. Draw a time line depicting all the cash flows associated with Sunrises view of the retirement annuity.

b. How large a sum must Sunrise accumulate by the end of year 12 to provide the 20-year, $42,000 annuity?

c. How large must Sunrises equal annual end-of-year deposits into the account be over the 12-year accumulation period to fund fully Mr. Lauren's retirement annuity?

d. How much would Sunrise have to deposit annually during the accumulation period if it could earn 10% rather than 9% during the accumulation period?

e. How much would Sunrise have to deposit annually during the accumulation period if Mr. Lauren's retirement annuity were a perpetuity and all other terms were the same as initially described?