You are given that = 0.08 and fT(x)T(y) (t, s) = t + s 8000 , 0 t, s 2

Two policyholders (x) and (y) have $100,000 to buy one of the following annuity: Annuity 1: a fully discrete special annuity of R is issued to (xy) and is payable for certain during 7 years. Annuity 2: a fully discrete annuity of K is payable during the first 3 years if (x) and (y) are alive. After 3 years, the annuity will pay (starting at time 3) K if their both alive, decreasing to 60%K on the death of (y), and decreasing to 40%K on the death of (x). Find R and K.