Suppose that our sample table applies to females and the mortality rate for males is 1.25 times that for females up to age 119. A is a male age 50 and B is a female age 40. The interest rate is a constant 5%.

(a) Find the level annual premium for an insurance paying 10 000 at the end of the year of first death of A and B with premiums payable while both are alive.

(b) Find the level annual premium for an insurance paying 10 000 at the end of the year of the death of A provided this occurs before the death of B. Premiums are payable while both are alive.

(c) Assuming UDD, find the probability that A will die before B.