Foundations of Actuarial Mathematics: Life Insurance and Annuities

Problem 7. .& moldorI An insurer issues a 20-year deferred annuity contract to a select age 50. 1 Joshop A . Level annual premiums will be paid for at most 10 years. dent 19hua . At age 70, provided the holder is still alive, an annuity of $10, 000 per year is paid annually in advance. pilog . If the holder survives 10 years, but dies before the first annuity payment, all pre- miums paid are returned without interest, at the end of the year of death. . There is no benefit payment on death in the first 10 years. oed to . Initial expenses are 1000 plus 30% of the first premium. . Expenses of 5% of the subsequent premiums.oriol esvinod [algal (s) You are given the following assumptions: . Mortality follows the Standard Select Life Table. . i = 0.05 . Premiums are calculated using the equivalence principle. (a) [5pts.] Determine P. (b) [5pts.] Find 5V. (c) [5pts.] Given the time length h = -0.05 and M70 = 0.00988, use Euler's method to find 19.95 V. (d) [5pts.] Suppose at the end of year 5, the policy is altered as follows: . the benefit is altered from a deferred annuity to a pure endowment payable on reaching age 70. . The cash value is equal to 90% of the policy value less a charge of $100. Calculate the altered benefit