Sunrise Industries wishes to accumulate funds to provide a retirement annuity fo

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 plancs 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. A) draw a time line depicting all of the cash flow associated with sunrise's view of retirement. B) how large a sum must Sunrise accumulate by the end of the year 12 to provide the 20 year 42.000 annuity? C) How large must sunrise's equal, annual, end of year deposits into the account be over 12 year accumulation period to fund fully Mr Moran retirement annuity? D) How much would sunrise have to deposit annually during the accumulation period if it could earn 10% rather 9 % during accumulation period? E) how much would sunrise have deposit annually during the accumulation period if Mr Moran's retirement terms were the same as initially described?

Explanation / Answer

Step#1: i = interest rate (.09) d = annual deposit (42000) n = number of years (20) p = present value (?) p = d(1 - k) / i where k = 1 / (1 + i)^n : that'll give you 383,398.92 Step#2: i = interest rate (.05) n = number of years (12) p = calculated above d = annual deposit (?) d = p(i) / j where j = (1 + i)^n - 1 : that'll give you 24,087.19 In case you're interested: you can combine the above 2 equations to get: d = 42000(.05)(1 - k) / (.09j) : that'll give you 24,087.19

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