# Question

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. 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.

a. 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?

d. How much would Sunrise have to deposit annually during the accumulation period if Ms. Moran’s retirement annuity were a perpetuity and all other terms were the same as initially described?

a. 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?

d. How much would Sunrise have to deposit annually during the accumulation period if Ms. Moran’s retirement annuity were a perpetuity and all other terms were the same as initially described?

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