How many Exam FM sample questions are there?

The SOA has published 456 sample questions for Exam FM, covering every section of the financial mathematics syllabus. FreeFellow hosts every one interactively with worked solutions.

Is Exam FM a calculator exam?

Functionally yes. Most live exam questions are solvable by setting up the right cash-flow structure on a BA-II Plus (or Casio approved equivalent) and executing the right button sequence. Fluency with the calculator is the practical difference between a 90-minute sitting and a 180-minute one. The SOA samples train this fluency by repeating the same cash-flow shapes with different inputs.

What topics do the 456 sample questions emphasize?

Annuities account for roughly 130 items (level, increasing, decreasing, deferred). Bond pricing and yield calculations account for about 100. Loan amortization and sinking funds account for 40. Term structure, forward rates, and immunization round out the rest with about 80 combined.

Are immunization problems on the FM samples?

Yes, but lightly. The asset-liability management subset is about 26 items, which is enough to learn the Redington and full-immunization conditions but not enough to drill them to mastery. Supplement with the FreeFellow original FM bank for additional immunization practice.

Can I practice the samples without a BA-II Plus?

Yes, but most candidates do their final-stretch practice on the same calculator they'll use on exam day to build button-sequence muscle memory. The TI BA-II Plus or Casio FC-200V are the two approved options.

Free Exam FM Sample Questions: 456 SOA-Published Items, Interactive (2026)

Exam FM Sample Questions, Free and Interactive

Exam FM is fundamentally a calculator exam. The math is approachable. The real test is whether you can recognize the cash-flow structure in front of you within 30 seconds and execute the right BA-II Plus sequence in the next 90. The SOA's 456 published sample questions train exactly that recognition.

FreeFellow reproduces all 456 inside an interactive practice surface. You select a choice, you get the worked solution alongside, your accuracy by topic feeds into the readiness score, and the adaptive engine re-surfaces the cash-flow patterns you keep tripping on. Free, no signup to browse, no credit card.

Start practicing Exam FM samples

What the 456 Sample Items Cover

The sample set is weighted toward where the live exam concentrates:

Topic area	Approx. sample count	What you'll see
Time value of money and interest theory	~80	Single cash flows, force of interest, varying interest, equivalent rates
Annuities	~130	Level (immediate, due, perpetuity), increasing, decreasing, deferred, varying continuously
Bond pricing and yield	~100	Par/premium/discount, yield to maturity, callable bonds, semi-annual coupons
Loans and amortization	~40	Constant payment loans, sinking fund method, varying payment loans
Cash-flow analysis	~50	IRR, NPV, time-weighted vs dollar-weighted returns, reinvestment risk
Term structure and forward rates	~30	Spot rates, forward rates, par yield curve, swap rates
Immunization and ALM	~26	Redington conditions, full immunization, Macaulay/modified duration, convexity

The recognizable patterns: annuity-immediate to annuity-due conversions show up in over half the annuity items. Bond yield-to-maturity calculations with semi-annual coupons appear in roughly half the bond items. Forward-rate triangulation (given two spot rates, find the forward) is the most common term-structure question shape.

Why FM Samples Train the Skill the Live Exam Actually Tests

The live FM exam isn't really testing your ability to derive financial-math formulas. It's testing whether you can:

Recognize a cash-flow structure in 30 seconds (level annuity, varying annuity, bond with sinking fund, loan with refinancing)
Pick the right BA-II Plus worksheet (TVM, BOND, CF, AMORT)
Execute the button sequence without keying errors
Sanity-check the result before locking in the choice

The SOA samples train all four. The repeated exposure to the same cash-flow shapes with different numerical inputs is what builds the recognition speed and the calculator fluency that separates a 90-minute sitting from a panic at minute 145.

Key Concept

FM is unforgiving on calculator errors. The samples include classic traps: bond yield where the coupon is paid in arrears versus advance, an annuity-due labeled as annuity-immediate in the stem, a sinking fund where the interest credit goes to the borrower rather than the lender. Working samples repeatedly is how you build the reflex to catch these on the live exam.

Three Tactics for the 456 Items

Build a calculator drill before you touch sample questions. Spend two hours doing pure mechanical drills on the BA-II Plus worksheets until N/I/Y/PV/PMT/FV are autopilot. Sample-question practice afterward is 3x more productive than starting cold.

Mix the bond and annuity items in your timed sets. The live exam shuffles cash-flow types. Working samples in topic order is fine for learning; working them mixed is what builds the type-switching speed live exam demands.

Drill the asset-liability management subset twice. The 26 ALM items are the most conceptually dense in the sample set. Most candidates score below 50 percent on these on the first pass. The second pass, with conscious attention to the immunization conditions (PV match, modified duration match, asset convexity higher than liability convexity), typically jumps to 80+ percent.

What the Samples Don't Cover Well

Honest gaps for FM:

Stochastic interest rate models. The 2025+ syllabus tilt toward stochastic models is sparse in the older sample batches. Lean on Marcel Finan's free FM textbook for additional drill here.
Newer-style portfolio yield problems. The dollar-weighted-versus-time-weighted distinction comes up on every live sitting but is light in the sample set.
Callable-bond pricing under interest-rate scenarios. Light coverage; supplement from the FreeFellow original FM bank.

How FM Practice Compares Across Free and Paid

Source	Exam FM Sample Questions	Format	Cost
FreeFellow	All 456, interactive	Same surface as topic practice	$0
ASM Financial Math Manual	All 456 in study manual	PDF in manual	$120 to $180
ACTEX Exam FM	Selected items + commentary	PDF in manual	$130 to $200
Coaching Actuaries Adapt FM	All 456 + originals + EL scoring	Interactive within Adapt	$200 to $300 per exam
Marcel Finan FM (free)	None	Free textbook with practice	$0
SOA only	All 456	Static PDF on soa.org	$0

Marcel Finan's free FM textbook deserves a callout: it's not the SOA samples but it's a free supplementary practice resource that pairs well with them.

Start Practicing

Practice all 456 Exam FM samples. For the broader FM study plan with weekly milestones: SOA Exam FM Study Guide. For the closely-related Exam P sample set: Free Exam P Sample Questions.