A deferred life annuity on (40) provides for a yearly income of 1000 beginning at age 65 and continuing for life. It is to be purchased by a single premium of S payable at age 40. If death occurs during the deferred period (i.e., during the first 25 years), then the single premium is refunded without interest at the end of the year of death.

(a) Give a formula for S using the symbols a and A.

(b) You are now given the following information. The same annuity contract without the premium-refund feature (i.e., nothing is paid during the deferred period) can be purchased for a single premium of 2000. In addition, a contract that provides the same annuity benefits, plus a level death benefit of 2000, payable at the end of the year of death, for death during the deferred period, can be purchased for a single premium of 2200. Calculate an exact numerical value for S.