A fully discrete 3-year temporary annuity immediate of 1000 with true semiannual payment is issued to (91.5). You are given that

k 0 1 2 3 4 5 6 7. 8. 9

k|q90 0.05 0.1 0.1 0.15 0.15 0.1 0.1 0.1 0.1 0.05

and d = 10%

(a) Define the present value random variable Y .

(b) Find the actuarial present value of this annuity under UDD.

(c) Determine the second moment of Y assuming constant force.

(d) Determine Pr [Y E[Y ]] under UDD.