1. A life insurance policy on (x) has level death benefits of 1000. A life insurance on (y) has exactly the same premiums and reserves as the policy on (x) for the first 10 years, but different death benefits. Suppose that qy+k = 2qx+k for k = 0, 1, ..., 9. If the common reserve 8V = 300, what is the death benefit on (y)'s policy for the year running from time 7 to time 8?
2. You are given that a81 = 3.2, q80 = 0.10, i = 0.20.
(a) Find a80.
(b) A single-premium whole life annuity on (80) provides for a constant benefit of 1 per year. Due to improvements in mortality, the actual mortality rate experienced during the first year of the contract is 0.07 rather than 0.1. On the other hand, the interest earned during that year was 22% rather than 20%. What is the total per contract gain for this year?