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. During her...

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. During her 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 and her family. Thus, they want to have a perpetuity which provide $15,000 each year (after the 25 year of retirement). During the 15-year “still working period” Sunrise wishes to fund the annuity by making equal annual end-of-year deposits into an account earning 9% interest. Once the 25-year “retirement period” begins, Sunrise plans to move the accumulated monies into an account earning a guaranteed 12% per year. After the 40th year, (after retirement) the interest rate will be 15%.  Note that all transaction will happen at the end of the year.

How large must Sunrise’s equal annual end-of-year deposits into the account be over the 15-year accumulation period to fund fully Ms. Asia Omar retirement annuity and perpetuity?