Fundamentals of Actuarial Mathematics (FAM) Exam
Life contingencies
Fundamentals of Actuarial Mathematics builds from survival models to insurance and annuity values. Know the survival function, force of mortality, life tables, curtate and complete future lifetimes, and select and ultimate mortality. For life insurance, distinguish term, whole life, endowment, and deferred products. For annuities, distinguish immediate, due, temporary, and deferred payments. The equivalence principle sets expected present value of premiums equal to expected present value of benefits plus expenses.
Reserves and traps
Reserves are prospective or retrospective values at a duration. The prospective reserve is the expected present value of future benefits and expenses minus future premiums. The retrospective reserve accumulates past premiums minus past benefits at interest. Traps include off-by-one timing at the start of a year, mixing continuous and discrete benefits, and forgetting that select mortality changes after the select period. Check whether death benefits are paid at the end of the year of death or at the moment of death.
Worked rule
For a whole life annuity-due of 1 per year on (x), the expected present value is a-double-dot-x = sum over k from 0 to infinity of v^k times kp_x. If mortality is uniform with q_x = 0.1 and i = 5%, the first term is 1, the second is (0.9)(1/1.05) = 0.8571, and later terms decay. The trap is using annuity-immediate timing. Write the payment dates first, then discount.