Confusing curtate and complete future lifetime

The curtate future lifetime K_x is the integer part of T_x (the complete future lifetime). Annuity values differ depending on which variable is used. Using the wrong one shifts the answer by up to half a year of payments.

Mixing up annuity-due and annuity-immediate notation

The life annuity-due (a-double-dot_x) has payments at the beginning of each year. The life annuity-immediate (a_x) has payments at the end. In LTAM, most standard formulas use the annuity-due. Using the immediate form without adjusting leads to errors.

Applying UDD when constant force is specified

Under UDD (uniform distribution of deaths), the fractional age survival probability interpolates linearly. Under constant force, it uses the exponential form. These give different results, and the problem statement specifies which assumption to use.

Errors in the recursive reserve formula

The recursion (tV + P)(1+i) = q_{x+t} * b_{t+1} + p_{x+t} * (t+1)V connects consecutive reserves. Forgetting to add the premium before applying interest, or using the wrong mortality rate, breaks the recursion.

Confusing net and gross premiums

Net premiums are calculated using the equivalence principle with benefits only. Gross premiums also include expenses and profit loading. Using net premium reserves when gross premium reserves are requested (or vice versa) gives the wrong answer.

Errors in multiple-decrement calculations

The probability of decrement j in the presence of all decrements differs from the associated single-decrement probability. Under UDD in the multiple-decrement table, the formulas for converting between them involve specific adjustments.

Forgetting the interest discount in insurance formulas

The actuarial present value A_x includes a discount factor v^(k+1) for whole life insurance. Omitting the discount factor or using the wrong power gives an overstated insurance value.

Not carrying enough decimal places in life table lookups

Rounding intermediate life table values too early causes the final answer to diverge from the listed choices. Carry at least 4 decimal places through intermediate calculations and round only at the end.

Misidentifying the status in multiple-life problems

Joint-life status (xy) pays on the first death. Last-survivor status (x-bar-y) pays on the second death. Selecting the wrong status in the formula leads to a completely different present value.

Rushing the written-answer section

Candidates who spend too long on multiple-choice questions leave insufficient time for written answers. Written answers offer partial credit, so even incomplete but well-organized solutions earn points. Budget your time carefully.

Common LTAM Mistakes