1. If 50 = 12.76 when = 0.06 , and 50 = 7.72 when = 0.1236 , what is the variance (nearest $1,000) of the present value random variable for a continuous life annuity of $100 per year issued to (50) at = 0.06 ? (a) 100,000 (b) 102,000 (c) 104,000 (d) 106,000 (e) 108,000

2. A special continuous life annuity issued to (50) is designed so that the payments continue until 10 years after the death of (50). If = 0.08 and mortality follows the pattern (x) = 0.04 for all x, what is the net single premium (given that e 0.8 = 2.22554 )? (a) 10.0 (b) 10.2 (c) 10.4 (d) 10.6 (e) 10.8

3. You are given (i) = 8 for all integral x (ii) = 0.08 Calculate 830 0 (a) 0.263 (b) 0.364 (c) 0.537 (d) 0.636 (e) 0.737

4. Y is the present value random variable for a 30-year temporary life annuity of 1 payable at the beginning of each year while (x) survives. You are given: (i) = 0.05 (ii) 30=0.7 0 (iii) :30 1 0 = 0.0694 2 (iv) :30 1 = 0.1443 Calculate [ 2 ] (a) 35.6 (b) 47.1 (c) 206.4 (d) 218 (e) 233.6

5. You are given (i) 1030 = 0.35 0 (ii) 30:9 = 5.6 (iii) = 0.10 Calculate 30:10 1 (a) 0.05 (b) 0.10 (c) 0.15 (d) 0.20 (e) 0.25

6. You are given: (i) = 0.22 (ii) +25 = 0.46 (iii) :25 1 = 0.20 (iv) = 0.06. Calculate :25 (a) 9.8 (b) 10.1 (c) 10.4 (d) 10.9 (e) 11.1

7. An annuity of 1, issued at age 35, is payable at the beginning of each year until age 65. The annuity payments are certain for the first 15 years. You are given: 15 = 11.94 35:15 = 11.62 35 = 21.02 30 = 19.60 35:30 = 18.13 50 = 15.66 65 = 9.65 Calculate the present value of the annuity. (a) 18.40 (b) 18.45 (c) 18.5 (d) 18.55 (e) 18.60

8. Mortality follows the Illustrative Life Table, = 0.06 Determine 65:10 (a) 10.1 (b) 10.4 (c) 10.7 (d) 11.0 (e) 11.3

9. You are given (i) 25:10 = 0.84 (ii) 25:20 = 0.69 (iii) = 0.02 Calculate 10|25:10 0 (a) 7.65 (b) 7.80 (c) 7.95 (d) 8.10 (e) 8.25

10. You are given (i) 10 = 0.40 0 (ii) 10| = 7 0 (iii) :10 = 15 Calculate .

11. Y is the present value random variable for a continuous life annuity of 1 on (x). You are given: (i) + = 0 (ii) = 5 (iii) 0 = 4 2 Calculate () (a) 15 (b) 25 (c) 35 (d) 45 (e) 55

12. You are given: (i) : 1 = 0.01419 (ii) = 0.54733 0 (iii) = 0.05 (iv) (4) = 1.00019 (v) (4) = 0.38272 Assume deaths are uniformly distributed over each year of age. Calculate : (4) (a) 8.83 (b) 9.00 (c) 9.04 (d) 9.10 (e) 9.38

13. You are given: (i) = 0.05 (ii) Deaths are uniformly distributed over each year of age. (iii) (2) = 14.500 (i) Calculate (2) (ii) Calculate