SOA Exam FM (Financial Mathematics) is a 2.5-hour computer-based exam with 30 multiple-choice questions, so you get five minutes per question. It covers the time value of money, annuities, loans, bonds, and general cash flows and portfolios, and it's usually the second exam actuarial candidates take.
FM was the second exam I took on my FSA path, and one of my favorites. Time value of money, annuities, loans and bonds all connect, and once you see how, the rest of the exam gets a lot easier.
What Exam FM covers
The current SOA syllabus splits FM into five sections:
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| Section | Weight | What's in it |
|---|---|---|
| Time value of money | 5-15% | Simple and compound interest, force of interest, discount rates, equations of value |
| Annuities and non-contingent cash flows | 20-30% | Annuity-immediate and annuity-due, deferred annuities, perpetuities, increasing and decreasing annuities, non-level payment streams |
| Loans | 15-25% | Amortization schedules, outstanding balance (prospective vs retrospective), principal and interest splits, drop and balloon payments, refinancing |
| Bonds | 15-25% | Bond pricing, amortization, callable bonds, yield measures |
| General cash flows, portfolios and asset-liability management | 20-30% | Yield rates, spot and forward rates and the yield curve, duration, convexity, immunization and cash flow matching |
Time value of money is the smallest section on paper, but everything else is built on it. If your fundamentals there are shaky, nothing else on the exam will make sense, so put the time in early. The annuity questions lean hard on setting up the equation correctly, especially telling annuity-immediate apart from annuity-due. Loan problems follow consistent patterns once you know the formulas, and the key skill is setting up the equation of value at the right point in time. Bond questions combine annuity calculations with present value, and the usual trap is a redemption value that differs from par, which the exam sets up on purpose.
Older FM guides, including an earlier version of this one, list derivatives (forwards, futures, put-call parity, swaps) as a topic. They aren't on the current FM syllabus, so you can skip them.
A 12-week plan
Start with the calculator. On Exam P a calculator helps but isn't essential. On FM the calculations are close to impossible by hand in the time you have, so the BA II Plus matters a lot. Spend 5 to 10 hours early on just drilling it, so you're not fumbling on exam day and losing minutes. Learn the TVM worksheet (N, I/Y, PV, PMT, FV), the cash flow worksheet for irregular cash flows, NPV and IRR, the amortization worksheet for principal and interest splits, and the bond worksheet for pricing and yield.
After that, the 12 weeks go roughly like this:
- Weeks 1 to 3: time value of money and annuities. Work 20 to 30 practice problems a day, practice the calculator until it's automatic, and focus on setting up equations of value at the right time point.
- Weeks 4 to 6: loans and bonds. Apply your TVM and annuity skills to harder problems, and pay attention to amortization schedules, since the exam likes asking for the interest part of the k-th payment.
- Weeks 7 to 9: general cash flows, portfolios and asset-liability management (duration, convexity, immunization), and start mixing topics.
- Weeks 10 to 12: full-length practice exams every 2 to 3 days, with targeted review in between.
Common mistakes and when you're ready
The most common calculation error I see is not matching periods: using a monthly interest rate with an annual annuity formula, or mixing up nominal and effective rates. Before you compute anything, check that your interest rate, payment frequency and time period are all in the same units. The exam also words timing ambiguously on purpose, so read carefully, because annuity-immediate and annuity-due give different answers.
For an outstanding loan balance, the prospective method (the present value of the remaining payments) is almost always faster than the retrospective one. Know both, but default to prospective.
You're ready for FM when you consistently score 70%+ on full practice exams, finish most problems in 5 minutes or less, can spot the right approach within seconds of reading a problem, don't have to think about the calculator, and have worked 800 to 1,200 practice problems. After 500+ problems you start seeing the same structures with different numbers, and that pattern recognition is what makes you fast on exam day.
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