Two lives age (x) and (y) are subject to the common shock model. T∗(x) has a constant hazard rate of 0.06, T∗(y) has a constant hazard rate of 0.04, and Z has a constant hazard rate of 0.02. The force of interest is a constant 0.05.

(a) Calculate A x(110) and write it as a sum of three terms, namely, the expected present value of benefits when: (i) (x) dies at a time strictly before the death of (y); (ii) (w) dies at time strictly after the death of (y); (iii) (x) dies as result of the common shock.

(b) Calculate A xy.