Exam FM technique guide
Learn how to recognize the method, recall the formulas that control it, and work through 54 sample-question solutions.
Try this original problem before opening the solution. Then compare the method with SOA Exam FM sample question 111.
Original practice · fully worked
An orchestra endowment pays 80 at each year-end forever. The education program receives the first N payments; all later payments support touring. At 4% effective, the touring stream is worth twice the education stream today. Determine N.
The ratio condition gives vᴺ = 2/3 and N = 10.34 years, choice C.
Setup
Both program values share the same payment amount, so the ratio depends only on the split date and discount factor.
Model
The later touring payments form a deferred perpetuity, while the education payments form a temporary annuity.
Compute
The ratio two reduces to v raised to N equal to two-thirds; logarithms give 10.338.
Answer
Thus the required split is about 10.3 years, choice C.
Calculator reproduction
Technique orientation
An annuity formula is a compressed cash-flow diagram. Its value depends on the payment dates, the valuation date, and the effective rate per payment period—not on the label attached to the financial story. Write the first and last payment times before choosing an annuity-immediate, annuity-due, deferred, varying, or perpetuity factor.
Exam FM frequently changes payment frequency, growth pattern, or deferral while leaving the underlying equation of value familiar. Level streams can often be checked on a BA II Plus TVM worksheet; irregular or varying streams are safer as an explicit sum or cash-flow worksheet. In both cases, the analytic timeline controls the calculator inputs.
Recognition audit
Before calculation
Name the requested quantity, mark its units or time point, and identify the assumption that permits the formula. Only then insert the numerical inputs. This separates model errors from arithmetic errors and makes the answer-choice comparison auditable.
Formula core
These identities are starting points, not substitutes for checking support, timing, rate periods, or independence assumptions.
Level annuity-immediate
The present-value factor sits one period before the first payment; the accumulated-value factor sits at the final payment date.
Annuity-due
Moving every payment one period earlier multiplies present value by 1 + i.
Level and growing perpetuities
P₁ is the payment one period after valuation; a payment at valuation must be handled separately.
Three failure modes to catch
Verified practice ledger
The list is grouped by current official syllabus area. Every link opens a step-labeled solution, verification artifact, distractor analysis, and one fully worked original variant.
54 verified references
Continue the study loop
The complete Exam FM manual includes all active sample-reference solutions, their wrong-choice analysis, and one independently written worked variant per reference. The free formula sheet is the compact companion for recall between practice sessions.
Related drills
Switch techniques when you can identify the current method before writing a formula and can explain each wrong-choice mechanism.
28 verified problems
Constant and variable force of interest, effective and nominal rate conversions, accumulation integrals, and 28 verified Exam FM solutions.
48 verified problems
Level-payment loans, prospective and retrospective balances, principal-interest splits, refinancing, and balloon payments.
31 verified problems
Macaulay and modified duration, convexity, price sensitivity, immunization, and portfolio weighting.
43 verified problems
Coupon-bond pricing, yield equations, premium and discount behavior, book values, and callable redemption dates.
