SOA Exam FM: Financial Mathematics

SOA Exam FM: Financial Mathematics

You’ll need to pass a total of 10 actuarial exams to be accredited as an actuary – life or non-life regardless.

Of course, the exams will be unique to the actuarial discipline you choose except for the first three – Exam P,  Exam FM, and Exam IFM. These are the exams that get you started on the path to actuary status.

As someone seriously looking into traveling the actuarial path, you must be adequately informed about these papers and all the small bits surrounding them. So in this post, you’ll be getting to learn more about SOA Exam FM – one of the preliminary exams.

What is it about? How to sign up for it? How do you prepare to write it? These and more questions are answered in this post.

Let’s go.

SOA Exam FM: What is it all about?

As mentioned above, Exam FM from the Society of Actuaries is one of the three preliminary professional actuarial exams. It is a multiple-choice test (so are the other two) that takes around 3 hours. You’ll encounter a total of 35 questions, each with A, B, C, D and E as the answer options.

For Exam FM study materials and question banks, click here:

For a larger part, it’s administered as a computer-based test.

And looking at its name – financial mathematics – you can get a hint of just what it is all about. Yes, it gives you as a candidate an understanding of important aspects of financial mathematics.

But it doesn’t stop there.

You also get exposed to the application of these financial mathematics aspects in determining the present and accumulated values for several streams of cash flows. This will prove crucial down the road in your actuarial work when you’ll be handling things like

  • Asset and liability management
  • Reserving
  • Pricing
  • Valuation
  • Investment income
  • Valuing contingent cash flows and
  • Capital budgeting.

But to grasp the said financial mathematics concepts, you should have a rough idea of both calculus and probability. The two feature prominently in handling the aforementioned concepts – and they don’t appear in Exam FM’s syllabus.

This isn’t much of a problem if you have a major in actuarial science, computer science, mathematics, economics, statistics or finance. Each one of them has one or more calculus and probability courses.

Not to worry though.

If your major had nothing to do with calculus or probability, you can take up classes on the same online.

That aside.

So we’ve mentioned that the core purpose of Exam FM is to teach you about financial mathematics. And as with any syllabus, the whole process of learning is broken down into several topics.

Exam FM – The Topics

SOA Exam FM’s syllabus comprises of 8 topics and each one of them contributes a certain percentage of questions to the exam. As you’ll see, some will take up a larger portion as compared to others. And still, some may fail to appear to feature in the test.

All the same, it’s always a good idea to polish up on each of these topics adequately no matter how much of the paper you’d expect them to take up. The percentages here are tentative; meaning they’re bound to change.

That’s that.

Over to the topics…

  1. Time value of money
  2. Annuities/cash flows with non-contingent payments
  3. Loans
  4. Bonds
  5. General cash flows and portfolios
  6. Immunization
  7. Interest rate swaps
  8. Determinants of interest rates

Have a look at what you’ll encounter in each of these topics below.

Time Value of Money

You can expect the time value of money to take up between 10 and 15% of the whole exam.

Its objective is to impact you with knowledge on current value, accumulated value, and present value. As a learner, you’ll get to know the ins and outs of these three important terms in addition to being able to work out related calculations.

So by the end of it all, here’s what is expected of you:-

  • Formulate an equation of value – in such a case; you’ll be given both an interest rate and a set of cash flows. You should know how to string them together correctly.
  • Be able to work out present value, future value, current value, interest rate or period of time. Usually, you’ll be given any three of these and be asked to work out any other one. You should be up to the task using either compound or simple interest. Additionally, you should be in a position to solve time value of money equations that feature a variable force of interest.
  • Have an understanding, and therefore be able to define the following terms: discount rate, convertible m-thly, interest rate, equation of value, inflation and real rate of interest, compound interest, current value, net present value, force of interest, simple interest, future value, discount factor, accumulation function, present value, effective rate and nominal rate.
  • Be able to find the value of any of the following: nominal discount rate convertible m-thly, effective interest rate, effective discount rate, force of interest, and nominal interest rate convertible m-thly. You’ll be given any one or more of these and asked to work out any other member of this list.

Annuities/Cash Flows with Non-contingent Payments

This second topic makes up 15-20% of the entire exam. Its prime focus is on current value, accumulated value and present value just like the first topic above.

The difference is that in this case, you’re working out these values specifically for sequences of non-contingent payments.

So what concepts should you be conversant with at the end of this topic? Take a look:-

  • Definitions of terms. Here are the terms you’ll encounter in this topic – geometric increasing /decreasing annuity, annuity due, term of annuity, arithmetic increasing/decreasing annuity, payable monthly/payable continuously, annuity immediate, perpetuity, and level payment annuity. You’re expected to not only be able to define them but to also be in a position to tie each one of them to their respective definitions.
  • And here are some types of annuity or cash flows you’ll bump into – level annuity with a finite term, level perpetuity and non-level annuities/ cash flow. Further on under non-level annuities, you’ll learn about those that follow arithmetic progression and those with a geometric progression and other types of non-level annuities. You may be given the interest rate, present value, current value, payment amount, future value an term of annuity in relation to the aforementioned cash flows. You should have the ability to find any of them using the provided information.


About 10 to 20% of all questions in this financial mathematics exam will be about loans. And yes, the topic is exactly what you’re thinking of – loans.

It builds you up on fundamental loan concepts and, of course, the accompanying calculations.

Here’s a quick overview of the loan concepts you should be aware of by the end of this topic:-

  • Definitions of important terms – have the meaning of the following terms at your fingertips: final payment (can be a drop or a balloon payment; know the distinction between the two), interest, amortization, term of loan, principle and outstanding balance. They’re the foundation so a thorough understanding of them can go a long way in cracking this topic.
  • After understanding the terms, it’s time for calculations. Concerning loans, you should have a knack for evaluating the outstanding balance at any given point in time and interest and principal for a particular repayment. Besides that, finding payment period, interest rate, principal, payment amount and term of loan given any 4 of them shouldn’t be a problem. Additionally, you must be in a position to perform calculations related to any of those mentioned in this bullet point in case refinancing is brought into the picture.


Pretty straightforward just like loans above. The name points clearly to what this whole topic is – bonds and contributes to about 10 to 20% of the exam questions.

You get a scoop of the important concepts and how to work out the related sums. So what are the expectations of you as a learner by the end of this topic? Glance over the following snippet to find out:-

  • You should be able to define the various bond-related terms, namely yield rate, term of bond, book value, redemption value, price, callable/non-callable, coupon and coupon rate, amortization of premium, par value/face value and accumulation of discount.
  • And of course, after getting an understanding of these terms, the next step is to do some calculations. This is what you’ll need to work out – price, book value, amortization of premium, accumulation of discount, yield rate, coupon and coupon rate, face value and redemption value, point in time that a bond has a particular book value and term of bond.

General Cash Flows and Portfolios

General cash flows and portfolios covers the nits and grits (that includes calculations) of rates of return, yield curves and measures of duration and convexity. These concepts will make up 15 to 20% of Exam FM.

So by the end of it all, the two parts that should have stuck in you are the definition of terms and the related calculations.

For definition, here are the terms you’ll have to deal with:-

  • Forward rate
  • Current value
  • Stock price
  • Stock dividend
  • Spot rate
  • Yield rate or rate of rate return
  • Yield curve
  • Portfolio
  • Dollar-weighted rate of return
  • Duration (Macaulay and modified
  • Time-weighted rate of return
  • Convexity (Macaulay and modified)

The calculation part here will involve the above definitions for a larger part. Nevertheless, check out this list of what you’d be expected to work out:-

  • The dollar-weighted rate of return as well as the time-weighted rate of return.
  • The present value of a given set of cash flows. For this, you’ll have to apply a yield curve derived from forward and spot rates.
  • Macaulay and modified duration. You’ll be given any one of them and asked to work out the other.
  • The price of a stock. Usually, you’ll have to apply the dividend discount model to accomplish this.
  • The resultant approximate change in present value due to a change in interest rate. Here, you’ll be expected to master two different ways of going about it – 1st-order linear approximation based on modified duration and 1st-order approximation based on Macaulay duration.


No, it has nothing to do with giving stabs – if that’s what you were thinking; at least not in the traditional sense.

You’ll get to explore the meaning and significance of immunization in the financial world in addition to cash flow matching – of course, including all the calculations that come with these two. These usually take up 10-15% of the whole paper.

As with the above topics, you’ll first be expected to be good with definitions before going to anything else. The essential definitions here are immunization, Redington immunization, and cash flow matching.

The second part of this topic is about building portfolios to meet various objectives. So you’ll be expected to be able to come up with an investment portfolio to:

  • Redington immunize a set of liability cash flows.
  • Exactly match a set of liability cash flows.
  • Fully immunize a set of liability cash flows.

Interest Rate Swaps

This topic equips you with an understanding of fundamental interest rate swaps concepts and how to evaluate related numerical problems. Sometimes questions on interest rate swaps may completely fail to feature anywhere in the exam. But usually, they may account for up to 10% of all the questions.

After this topic, it’ll be assumed that you can define

  • Market value of a swap
  • Counterparties
  • Accreting swap
  • Swap rate
  • Settlement dates
  • Interest rate swap net payments
  • Notional amount
  • Amortizing swap
  • Deferred swap
  • Swap term/swap tenor

Aside from the definitions, you should be able to calculate the following items of an interest rate swap

  • Market value
  • Notional amount
  • Spot rates
  • Swap rate

The swap here may either be deferred or not and can have a constant or varying notional amount.

Determinants of Interest Rates

Finally, the last topic – determinants of interest rates. It’s tested with the same frequency as the interest rate swaps above – that’s between 0-10 percent of the entire exam.

As per the name, the topic is all about important concepts about determinants of interest rates. Additionally, you’ll meet other concepts about the components of interest; and calculations, of course.

After going through this topic, here are the boxes you should have ticked

  • An understanding of different components of interest rates – things like liquidity premium, real risk-free rate, maturity risk premium, inflation rate, and default risk premium.
  • Applications of these components in a range of scenarios like credit cards, mortgages, commercial loans, etc.
  • Knowledge of why there is variation in interest rates across different countries
  • An explanation of why interest rates differ by term, liquidity preference or opportunity cost, expectations, market segmentation, and preferred habitat.
  • Identification of the real interest rate and the nominal interest rate for loans – in the presence or absence of inflation protection. Under this, you should be able to calculate the effect changes in inflation will have on loans with inflation protection.
  • An understanding of the roles of the Federal Reserve and the Federal Open Market Committee (FOMC) in executing fiscal policy. You should also know the tools used by these two bodies, for example setting reserve requirements and discount rate, etc.

All said about the topics said, be sure to keep an eye out on any updates on this syllabus. This page will keep you in the know in case of any changes.

Moving on…

Registering for Exam FM

If you’re considering registering for Exam FM, you need to be informed of the process, the dates during which the registration is open, and the payment details – that is the amount and methods of remittance accepted by SOA.

Each one of them is dissected in detail below.

The Process

The process is pretty easy – and can be done either online via the SOA website or filling forms and then sending them over. The choice of the method you use depends on your preference.

But it’s easy to see which one of them is better, right?

Whatever your choice, you should keep an eye on that deadline. Naturally, you won’t be accepted if you turn in your information later than the indicated date. The open period usually closes at midnight US Central Time.

That aside, make sure the names you’ll give tally with those on the official identification document you’ll provide – the spellings and the order. Any discrepancies will see your application thrown out.

After handing over your details, you’ll receive an acknowledgment letter with an inactive candidate/eligibility number. This number will be activated in a space of 3-5 business days upon which SOA will send you a letter of confirmation.

And that means you’re in.

So it will be time for you to take the next step – schedule an appointment at a CBT Prometric center. You have 2 options through which you can do this:

  1. By telephone – you just ring the Prometric’s Candidate Services Contact Centre and reference SOA/CIA exams. Find the full contact list on this page.
  2. Online – every step will be available to you once you land on All you need is to follow through and you’ll be done in no time.

But it’ll be meaningless to attempt any of these steps out of the registration window. That’s why you need to keep tabs on the dates.


The registration period runs for 6 weeks (approximately 2 months) before the exam window. So if you want to determine when to register, pinpoint the exam date (usually published on the SOA website) and counting back 6 weeks.

Or you can skip all this by following the lead from SOA on this page.


Of course, there is a cost in sitting for Exam FM – you must pay a sum of $225.

This amount can be paid via any of the following payment methods accepted by SOA-

  • Master Card
  • Visa
  • American Express.

Considerations for Candidates with Special Needs

You should request testing accommodation if you have any condition that affects your ability to sit for exams under the normally provided environment.

And this shouldn’t be a problem as long your case is genuine and doesn’t impact the whole exam process negatively; like giving you an unfair advantage. Read the testing accommodations fine print to get more information about this.

Preparing for Exam FM

Done with the registration? Now it’s time to gear up for the exam. And it can be an intensive process if you’re doing it alone. That’s why a bit of hand-holding can work wonders.

Here at Analyst Prep, we offer the material and required guidance so that you have all it takes to sit for Exam FM. Here’s a full range of what you’ll have by studying with us. Click here to have a look at all our Exam FM study materials:

Some spoiler – you get to learn from people who’ve exactly in the same spot as you are right.

On the Exam Day

After months of trying to (successfully and unsuccessfully) figure out concepts, you’ll have to turn up and put to good use what you gained – at the Prometric center you chose.

As you’d expect, there are rules and regulations set by SOA to ensure everything runs smoothly.

In a nutshell, these guidelines define the exam-related items to have, your conduct in and outside the testing room and so on.

For instance, you have to turn up early enough at the center to allow enough time for some procedures – like verification. Any lateness may mean that you forfeit your chance to sit for the exam.

Check out the comprehensive rules and regulations on this page.

How’s Exam FM Graded?

Grading for Exam FM is similar to Exam P.

Scores are evaluated on a scale of 0 to 10. The values that matter start at 6 to 10 – this is the pass mark. So you know where to aim for prospective actuary, don’t you?

Getting Your Exam FM Scores

As with all SOA exams, you can get to know your Exam FM scores via Online Transcript Access on SOA’s website. You have to give it time though.

It usually takes 8-11 weeks for scores to be available and another week later for the list of passing candidates to be released.


Planning to sit for Exam FM? Let this post guide you through all the steps you’ll take. Everything is simplified for your understanding.

Don’t just sit on the information – get out there and make arrangements. The world needs your actuarial skills.