IFoA CM1 common mistakes
IFoA CM1 · Understand the traps and how to avoid them.
When a question gives a force of interest δ(t) or a time-varying rate, candidates plug the rate into (1+i)^n or apply v^n directly instead of computing the accumulation as exp(∫δ(s)ds) over the actual limits, and they mis-handle the limits when the cashflow starts at a time other than 0.
Most practice is done with level rates, so the compound-interest formula becomes automatic. Under exam pressure the familiar formula is retrieved before the candidate checks whether the rate is constant, and the integral is then skipped or its limits are copied from a level-rate template.
What to do instead
Before any calculation, write down the accumulation factor symbolically as A(t1,t2)=exp(∫ from t1 to t2 of δ(s)ds) and only then substitute. Practise a mixed set where the same cashflow is valued under constant, linear and piecewise δ so the general form stays the default. When discounting a payment at time t back to time 0, always split the integral at every point where δ changes.
Candidates build an equation of value using the wrong focal date, mixing payments accumulated forward and discounted backward inconsistently, and then solve for the unknown rate or payment from an equation that is not dimensionally consistent in time.
The arithmetic of discounting feels mechanical, so the focal date is chosen implicitly and forgotten. When a question asks for a yield, the candidate also forgets that the resulting polynomial may have multiple roots or that the answer must be checked against the direction of the cashflows.
What to do instead
State the focal date explicitly at the top of the working and label every term with its time offset before computing. For yield problems, write the net present value as a function of i, note the sign pattern of the cashflows, and check whether a unique positive root is plausible. Verify by revaluing at a second focal date; the answer must be identical.
For annuities, candidates use a-due and a-immediate formulae interchangeably, misapply the accumulated value versus present value notation, and mishandle annuities where the term, the payment frequency and the interest conversion period differ (for example monthly payments with annual effective interest).
The notation a-angle-n, ä-angle-n, s-angle-n and the double-dot variants look similar and are memorised as a block. Payment frequency mismatches are treated as a detail rather than a change of model, so the candidate converts the interest rate incorrectly or forgets to convert at all.
What to do instead
Adopt a fixed habit: draw a time line, mark the first and last payment, and decide due versus immediate from the picture rather than from memory. For frequency mismatches, convert to an equivalent rate per payment period using (1+i)=(1+i^(p)/p)^p and state the conversion in the working. Sanity-check the answer against the limiting cases of a perpetuity and a single payment.
In present-value random variable questions, candidates compute only the expected present value and stop, ignoring that the question asks for the variance, the distribution function, or the probability that the present value exceeds a threshold. They also treat the sum assured as paid at the moment of death when the contract pays at the end of the year of death, or vice versa.
EPV is the most rehearsed calculation, so the candidate reads the first few words of the question and starts the familiar computation. The timing convention (continuous versus discrete) is buried in the contract description and is easy to skim past.
What to do instead
Before computing, underline the payment timing and the quantity requested. If a variance or probability is needed, write the present-value random variable explicitly as a function of the future lifetime and derive its distribution from the life table rather than working only with moments. Keep a one-page comparison of continuous and discrete assurance EPVs with their variances and refer to it until the timing conventions are automatic.
Candidates apply a single-decrement life table directly to a multiple-decrement situation, treating the crude rate of decrement from one cause as if it were the independent rate, or they fail to convert between dependent and independent rates when the question requires it.
The life-table mechanics (l_x, d_x, q_x) are heavily practised in the single-decrement setting, and the multiple-decrement adjustment looks like a small variation. The distinction between the force of decrement in the presence of other causes and the underlying independent rate is conceptually thin and easily collapsed.
What to do instead
Learn the relationship between the dependent rate q_x^(j) and the independent rate q_x^(j)* explicitly, including the approximation and the exact form under constant forces, and practise converting in both directions. When a question mentions more than one cause of exit, write down which rates are given and which are required before touching numbers.
In multiple-state models, candidates compute transition probabilities by multiplying the one-step transition intensities over the period, ignoring that a person can move back and forth between states and that the probability of being in a state at time t is not simply the product of the direct path probabilities.
The Markov chain machinery is new relative to the life-table material, and the matrix exponential or the Kolmogorov forward equations are intimidating, so candidates substitute a simpler product that works only for acyclic, single-path models.
What to do instead
For any multi-state question, set up the generator matrix and identify whether the model is acyclic. If it is acyclic, path products are valid and should be used. If it is not, use the matrix exponential or solve the forward equations, and check that the row sums of the transition probability matrix equal one as a numerical check.
When computing gross premiums and reserves, candidates use the wrong basis: they mix the premium basis with the valuation basis, forget to include initial expenses and renewals consistently, or compute a net premium reserve when the question asks for a gross premium reserve (or the reverse).
The formulae differ only in which cashflows are included, so under time pressure the candidate reuses whichever formula was last practised. The distinction between the net premium and the gross premium, and between the office premium and the valuation premium, is a definitional point that does not produce an obviously wrong-looking number.
What to do instead
At the start of every premium or reserve question, write a short list of the cashflows included in the basis being used (benefits, premiums, initial expense, renewal expense, commission) and tick them off as they enter the equation. State the reserve definition being used (prospective or retrospective) and confirm that the premium used in the reserve is the one appropriate to that definition.
In profit-testing questions, candidates project cashflows but omit or double-count items such as the release of reserves, interest earned on reserves, and the emergence of profit, and they discount the resulting profit vector at the wrong rate or from the wrong time origin.
Profit testing is a bookkeeping exercise with many lines, and the reserve appears both as a cost when it is set up and as a release when it is freed. Candidates follow the layout of a worked example without understanding which items are inflows and which are outflows.
What to do instead
Build the profit test from first principles each time: premiums in, benefits, expenses and increases in reserves out, then interest on the opening fund. Track the reserve as a stock, not a flow, and check that the closing reserve equals the opening reserve plus the increase. Discount each year's profit from the end of that year and confirm the time origin before discounting.
On reserving and solvency questions, candidates compute a reserve or a capital requirement without stating the basis, ignore the difference between best-estimate and prudent assumptions, and fail to relate the result to the supervisory or economic capital framework described in the question.
The numerical part of the question is familiar, so the candidate treats the surrounding regulatory description as context to be skimmed. The link between the assumptions chosen and the purpose of the calculation (statutory reserve versus economic capital versus embedded value) is not made explicit.
What to do instead
Read the question for the purpose of the calculation and the regime named, then select assumptions that match that purpose and say so in the answer. Where the question asks for a comparison, structure the answer around the assumptions, the discount rate and the risk margin separately. Practise writing short justification sentences alongside the numbers, since marks are often awarded for the basis rather than the arithmetic.
In pension and social security questions, candidates model the scheme as if it were an individual life insurance policy, applying the same premium and reserve logic without accounting for salary scales, final-salary definitions, accrual rates, or the difference between funding on a projected benefit basis and a current-unit basis.
The life insurance framework is the dominant mental model from earlier questions, and the pension material is often revised last. Terms such as accrual rate and salary scale are recognised but not connected to the cashflow model.
What to do instead
Write down the benefit formula explicitly (for example accrual rate times years of service times final or average salary) and derive the projected benefit before valuing it. Distinguish the projected unit credit, current unit and aggregate funding methods by what they value, and practise a small numerical example for each. Check whether the question asks for the cost to the employer, the value of the member's accrued benefit, or the scheme's funding level, since these require different calculations.