1 Suppose that the mortality pattern of (2) is defined by the following force of mortality: Patt for 0

Suppose that the mortality pattern of (x) is defined by the following force of mortality: for 0 < t < 100 x. You are given that = 0.05 and 19.004. 100-xl Questions: 1. Using the fact that 19.004, show that x 100-xl = 40. of 4 2. Prove the following expression for the survival probabilities : for 0 < s < 60 t. sp40+t = I 60-t ' 3. Prove the following relation for A40+t: A40_+t = 60t a60tl 4. Consider a life assurance contract where the expected present value of benefits is 1, OOOAC, the expected present value of premiums is Px, and no expenses are included. Determine the numerical value of the premium P of this contract using the principle of equivalence. 5. Derive a general formula for the prospective reserve t v at time t as a function of P, and A40+t. 6. When will the reserve be equal to zero? 7. Give the numerical value of the reserve at time t