SOA Exam FM Practice Exam and Practice Problems
Work original Exam FM problems on interest rates, annuities, loans, bonds, yield curves, duration and immunization, read the full solution, then sit a timed 30-question practice exam in the CBT format: 2.5 hours, five answer choices per question.
30 questions, five answer choices each, 2.5 hours, with a score by syllabus topic and a worked solution for every problem.
Or start with a free 10-question drill- 278 original Exam FM problems with worked solutions
- 9 free drills: every syllabus topic plus a mixed set
- 45.7% of candidates passed in August 2026
A 20-year loan is repaid with level annual payments at the end of each year at an annual effective rate of 9%. Calculate the number of the first payment whose principal portion exceeds its interest portion.
Exam FM exam format
- Questions
- 30 multiple-choice questions, 5 answer choices each (A to E), one correct. A few unscored pilot questions are mixed in; unanswered questions count as wrong
- Time
- 2.5 hours, about 5 minutes a question
- Where
- Computer-based at Prometric test centers
- 2027 windows
- February 4–15 · April 1–12 · June 10–21 · August 5–16 · October 1–12 · December 2–13
- Calculators
- Approved models only: BA-35, BA II Plus, BA II Plus Professional, TI-30Xa, TI-30X II (IIS solar or IIB battery) and TI-30XS MultiView (or XB battery)
- Pass mark
- Set before each exam by item response theory; 71% on recent computer-based sittings
- Pass rate
- 45.7% of 2,648 candidates in August 2026
- Fee and results
- $275 per sitting, paid to SOA. An unofficial pass or fail result by email within one hour
What’s on Exam FM
The 5 topics of the current SOA syllabus with their weights, and the drills that cover them. Our practice exam draws its 30 questions in proportion to the middle of each weight range. Every drill opens with a study guide, then ten problems with a worked solution after every answer; each drill’s first attempt is free.
| Syllabus topic | Weight | Drills and study guides |
|---|---|---|
| 1. Time Value of Money | 5–15%3 of 30 in our exam | |
| 2. Annuities and cash flows with non-contingent payments | 20–30%8 of 30 in our exam | |
| 3. Loans | 15–25%6 of 30 in our exam | |
| 4. Bonds | 15–25%6 of 30 in our exam | |
| 5. General Cash Flows, Portfolios and Asset Liability Management | 20–30%7 of 30 in our exam |
Exam FM study guide by topic
Interest rates and the time value of money
Simple and compound interest, nominal and effective rates of interest and discount, the force of interest, inflation and equations of value.
- Convert every rate to one effective rate per payment period before you do anything else: (1 + i⁽ᵐ⁾/m)ᵐ = 1 + i = (1 − d)⁻¹ = e^δ.
- With a varying force of interest, the accumulation factor from s to t is exp(∫ from s to t of δ(r) dr).
Level annuities and perpetuities
Annuities-immediate and annuities-due, deferred annuities, perpetuities, payments m-thly or continuously, and solving for the term or the rate.
- aₙ⌉ = (1 − vⁿ)/i and äₙ⌉ = (1 + i)·aₙ⌉; a perpetuity-immediate is worth 1/i, a perpetuity-due 1/d.
- Match the payment period to the rate: monthly payments need the effective monthly rate.
Increasing, decreasing and geometric annuities
Arithmetic increasing and decreasing annuities and perpetuities, geometric annuities and other non-level cash flows.
- (Ia)ₙ⌉ = (äₙ⌉ − nvⁿ)/i and (Da)ₙ⌉ = (n − aₙ⌉)/i; a payment pattern P, P + Q, … is P·aₙ⌉ + Q·(aₙ⌉ − nvⁿ)/i.
- An increasing perpetuity-immediate paying 1, 2, 3, … is worth 1/i + 1/i².
Loans and amortization
Amortization schedules, outstanding balances, the interest and principal in a payment, drop and balloon payments, and refinancing.
- The balance just after payment k is the present value of the remaining payments (prospective) or the accumulated loan minus the accumulated payments (retrospective).
- For a level-payment loan, the principal in payment k is P·v^(n − k + 1) and the interest is P·(1 − v^(n − k + 1)).
Bonds
Bond price, book value, premium and discount amortization, yield, coupon and redemption values, callable bonds and reinvested coupons.
- Price = Fr·aₙ⌉ + C·vⁿ at the yield j per coupon period; premium/discount form: P = C + (Fr − Cj)·aₙ⌉.
- The amortization of premium in coupon k is (Fr − Cj)·v^(n − k + 1); book value moves toward C over the bond’s life.
Yield rates, spot and forward rates
Net present value and internal rate of return, spot rates, forward rates and yield curves, and pricing cash flows from a yield curve.
- Discount each cash flow at the spot rate for its own time: PV = Σ CFₜ/(1 + sₜ)ᵗ.
- The one-year forward rate from t − 1 to t is (1 + sₜ)ᵗ/(1 + sₜ₋₁)^(t − 1) − 1.
Duration and convexity
Macaulay and modified duration and convexity of a set of cash flows and portfolios, and first-order approximations of price changes.
- Macaulay duration is the present-value-weighted average time of the cash flows; modified duration = Macaulay duration / (1 + i).
- First-order modified approximation: P(i₁) ≈ P(i₀)[1 − (i₁ − i₀)·D_mod]. Macaulay approximation: P(i₁) ≈ P(i₀)·((1 + i₀)/(1 + i₁))^D_mac.
Immunization and cash-flow matching
Redington immunization, full immunization and exact cash-flow matching of liabilities with bonds.
- Redington immunization: PV(assets) = PV(liabilities), equal durations (first derivatives) and asset convexity greater than liability convexity.
- Full immunization of a single liability needs one asset cash flow before it and one after, with matching present value and duration.
What Exam FM tests
- Annuities (20% to 30%) and general cash flows, portfolios and asset-liability management (20% to 30%) carry the most weight: level and varying annuities, spot and forward rates, duration, convexity and immunization.
- Loans and bonds carry 15% to 25% each: amortization, outstanding balances, refinancing, bond prices, book values, yields and callable bonds.
- Time value of money (5% to 15%) is the base for every other topic: nominal and effective rates of interest and discount, the force of interest and equations of value.
Common questions
How many questions are on SOA Exam FM?
30 multiple-choice questions in 2.5 hours, taken on a computer at a Prometric test center. Each question has five answer choices, A to E, with one correct answer, and a few unscored pilot questions are mixed in.
What is the passing score for Exam FM?
SOA sets the pass mark before each exam using item response theory and publishes it with the results. Recent computer-based sittings list a pass mark of 71%, about 21 to 22 of the 30 questions, though a few unscored pilot questions sit among the 30. Unofficial pass or fail results are emailed within one hour of the exam.
What calculators can I use on Exam FM?
Only the SOA-approved models: BA-35, BA II Plus, BA II Plus Professional, TI-30Xa, TI-30X II (IIS solar or IIB battery) and TI-30XS MultiView (or XB battery). You may bring more than one approved calculator; for the BA II Plus models and the TI-30X IIS, TI-30XB and TI-30XS MultiView, you show the supervisor that the memory is cleared.
How long is Exam FM?
2.5 hours for 30 multiple-choice questions, about 5 minutes a question. Each question has five answer choices, A to E, and unanswered questions are scored as wrong, so answer every one.
Are these official SOA questions?
No. These are original practice problems written to the current SOA syllabus, with every answer recomputed independently in code and a worked solution for every problem. They are not SOA sample questions.
When is Exam FM offered?
Six times a year in even months. The 2027 windows are February 4–15, April 1–12, June 10–21, August 5–16, October 1–12 and December 2–13; registration closes about a month before each window. The fee is $275.
What is the Exam FM pass rate?
45.7% of the 2,648 candidates passed the August 2026 sitting, with a 71% pass mark, according to SOA’s result sheet.
Are interest rate swaps on Exam FM?
No. The current syllabus has five topics: time value of money, annuities, loans, bonds, and general cash flows, portfolios and asset-liability management. Swaps and the determinants of interest rates are not on it, and bonds are not valued between coupon dates.
Ready for exam day?
30 questions, five answer choices each, 2.5 hours, with a score by syllabus topic and a worked solution for every problem.
Or start with a free 10-question drillMore SOA exam practice
One Exam P and FM pass covers both timed practice exams and unlimited drills.
Exam format, fees, syllabus, dates and pass rates checked November 2026: SOA Financial Mathematics Exam syllabus (February 2027) · SOA August 2026 Exam FM results · SOA: Probability (P) Exam · SOA: Financial Mathematics (FM) Exam · SOA exam schedule · SOA: identification and approved calculators.
Original independent practice problems written to the published SOA syllabus. Not affiliated with or endorsed by the Society of Actuaries (SOA).