Sunrise Industries wishes to accumulate funds to provide a retirement annuity for its vice president of research, Asia Omar. Ms. Omar by contract will retire at the end of exactly 15 years. Upon retirement, she is entitled to receive an annual end-of-year payment of $50,000 for exactly 25 years. If she dies prior to the end of the 25-year period, the annual payments will pass to her heirs.
Also sunrise want to assure a stability life for Asia Omar. Thus, they want to have a perpetuity which provide $15,000 each year. 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 accumulat ed monies into an account earning a guaranteed 12% per year. After the 40th year, the interest rate will be 15%.
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 15.
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. Asia Omar retirement annuity and perpetuity?