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“Sunrise Industries wishes to accumulate funds to provide a retirement annuity for its vice president of research, Jill Moran. Ms. Moran, by contract, will retire at the end of exactly 12 years.

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 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,” Sunrise 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, Sunrise plans to move the accumulated monies to 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 first distribution payment will be received at the end of year 13.TO DOa. How large a sum must Sunrise accumulate by the end of year 12 to provide the 20-year, $42,000 annuity?b. How large must Sunrise’s equal, annual, end-of-year deposits into the account be over the 12-year accumulation period to fund fully Ms. Moran’s retirement annuity?c. How much would Sunrise have to deposit annually during the accumulation period if it could earn 10% rather than 9% during the accumulation period?

 

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