[[Actuarial Notes Wiki|Wiki]] / **Exam FM-2 (SOA)** ## Exam FM-2 Syllabus <div class="exam-nav" data-color="#4f46e5" data-prev="P-1|Probability|Exam P-1 (SOA).md" data-current="FM-2|Financial Mathematics|" data-next="FAM|Fundamentals of Actuarial Mathematics|Exam FAM (SOA).md|SOA,MAS-I|Modern Actuarial Statistics I|Exam MAS-I (CAS).md|CAS" data-tracks="ASA|Associate of the Society of Actuaries (ASA).md,ACAS|Associate of the Casualty Actuarial Society (ACAS).md" </div> The **Financial Mathematics (FM-2) Exam** is a 2.5 hour exam with 30 multiple choice questions about financial mathematics concepts and how they are applied in calculating present and accumulated values for streams of cash flows. <div class="callout-cols-2"> > [!answer]- 📅 Exam Schedule {2026} > > Dates | Exams > -|- > Apr 2-13 | FM >Jun 11-22 | FM >Aug 6-17 | FM >Oct 1-12 | FM >Dec 3-14 | FM > >- [Register for Exam FM](https://www.soa.org/education/exam-req/registration/edu-registration/) > [!answer]- 📄 Download Resources {4 Files} > - [April 2026 Exam FM Syllabus](https://www.soa.org/globalassets/assets/files/edu/2026/spring/syllabi/2026-04-exam-fm-syllabus.pdf) > - [June 2026 Exam FM Syllabus](https://www.soa.org/globalassets/assets/files/edu/2026/syllabi/2026-06-exam-fm-syllabus.pdf) > - [462 Sample Questions for Exam FM (SOA)](https://www.soa.org/globalassets/assets/files/edu/2018/2018-10-exam-fm-sample-questions.pdf) > - [462 Sample Answers for Exam FM](https://www.soa.org/globalassets/assets/files/edu/2018/2018-10-exam-fm-sample-solutions.pdf) </div> > [!answer]- 📕 Source Material {5 Textbooks} > |Source|Coverage| > |---|---| > |[[Mathematics of Investment and Credit (Broverman, S.A. – 2024)]]|Chapters 1–7^[excluding 1.2.1, 1.8; 2.3.1.2, 2.4.2, 2.4.3, 2.4.5; 3.2.1, 3.2.2, 3.3, 3.4; 4.1.3, 4.1.4, 4.4 (background only); 5.2, investment year method portion of 5.3.1, 5.3.2–5.3.4; 6.2, 6.4; 7.1.3, 7.3]| > |[[Mathematical Interest Theory (Vaaler, L.J.F., Harper, S.K., and Daniel, J.W. – 2019)]]|Chapters 1–6, 8–9^[excluding 1.13–1.16; 2.6; 3.10, 3.12, investment year method portion of 3.13; 5.3; 6.6–6.7, example 6.8.1, 6.10; Ch. 8: 8.3 only; 9.4, 9.5, 9.7]| > |[[Financial Mathematics: Theory and Practice (Brown, R. and Kopp, S. – 2024)]]|Chapters 1–9^[Ch. 2: sections 1–3 only; Ch. 4: sections 1, 3–5 only; Ch. 7: sections 1–2 only]| > |[[Interest Theory – Financial Mathematics and Deterministic Valuation (Francis, J. and Ruckman, C. – 2022)]]|Chapters 1–16^[excluding 14.04 and 14.05]| > |[[Financial Mathematics for Actuaries (Chan, Wai-Sum, and Tse, Yiu-Kuen – 2022)]]|Chapters 1–8^[excluding 2.4; 3.5; 4.2, 4.5; 5.3; 6.4; 8.6, 8.7, 8.8]| ### Learning Objectives > [!example]- Time Value of Money {5-15%} > ### Time Value of Money > Understand and be able to perform calculations relating to [[Present Value]], [[Current Value]], and [[Accumulated Value]]. > 1. Define and recognize the definitions of the following terms: [[Interest Rate]] (rate of interest), [[Simple Interest]], [[Compound Interest]], [[Accumulation Function]], [[Future Value]], current value, present value, [[Net Present Value]], [[Discount Factor]], [[Discount Rate]] (rate of discount), [[Convertible m-thly]], [[Nominal Rate]], [[Effective Rate]], [[Inflation]] and [[Real Rate of Interest]], [[Force of Interest]], [[Equation of Value]]. > 2. Given any three of **interest rate**, **period of time**, **present value**, and **future value**, calculate the remaining item using **simple** or **compound interest**. Solve [[Time Value of Money Equations]] involving [[Variable Force of Interest]]. > 3. Given any one of the **effective interest rate**, the [[Nominal Interest Rate Convertible m-thly]], the [[Effective Discount Rate]], the [[Nominal Discount Rate Convertible m-thly]], or the **force of interest**, calculate any of the other items. > 4. Write the **equation of value** given a set of **cash flows** and an **interest rate** > [!example]- Annuities/Cash Flows with Non-Contingent Payments {20-30%} > ### Annuities/Cash Flows with Non-Contingent Payments > 1. Define and recognize the definitions of the following terms: [[Annuity-Immediate]], [[Annuity Due]], [[Perpetuity]], [[Payable m-thly]] or [[Payable Continuously]], [[Level Payment Annuity]], [[Arithmetic Increasing/Decreasing Annuity]], [[Geometric Increasing/Decreasing Annuity]], [[Term of Annuity]]. > 2. For each of the following types of **annuity**/**cash flows**, given sufficient information of **immediate** or **due**, **present value**, **future value**, **current value**, **interest rate**, **payment amount**, and term of annuity, calculate any remaining item. > - [[Level Annuity]], finite term. > - [[Level Perpetuity]] > - [[Non-level Annuities]]/cash flows. > - [[Arithmetic Progression]], finite term and perpetuity. > - [[Geometric Progression]], finite term and perpetuity. > - Other non-level annuities/cash flows. > [!example]- Loans {15-25%} > ### Loans > Understand key concepts concerning [[Loans]] and how to perform related calculations. > 1. Define and recognize the definitions of the following terms: [[Principal]], [[Interest]], [[Term of Loan]], [[Outstanding Balance]], [[Final Payment]], [[Drop Payment]], [[Balloon Payment]][[Amortization]] > 2. Calculate: > - The missing item, given any four of: **term of loan**, **interest rate**, **payment amount**, **payment period**, **principal**. > - The **outstanding balance** at any point in time. > - The **amount of interest** and **principal repayment** in a given payment. > - Similar calculations to the above when refinancing is involved. > [!example]- Bonds {15-25%} > ### Bonds > Understand key concepts concerning [[Bonds]], and how to perform related calculations. > 1. Define and recognize the definitions of the following terms: [[Bond Price|Price]], [[Book Value]], [[Market Value]], [[Amortization of Premium]], [[Accumulation of Discount]], [[Redemption Value]], Par Value/[[Face Value]], [[Yield Rate]], [[Coupon]], [[Coupon Rate]], [[Term of Bond]], [[Callable Bond|Callable]]/[[None-Callable Bond|Non-Callable]], [[Call Price]], [[Call Premium]], [[Accumulated Value]] with [[Reinvestment of Coupons]]. > 2. Given sufficient partial information about the items listed below, calculate any of the remaining items > - Price, book value, market value, accumulated value with reinvestment of coupons, amortization of premium, accumulation of discount. (Note that valuation of bonds between coupon payment dates will not be covered). > - Redemption value, face value. > - Yield rate > - Coupon, coupon rate > - Term of bond, point in time that a bond has a given book value, amortization of premium, or accumulation of discount > 3. Calculate the price of a callable bond to achieve a specified minimum yield > [!example]- General Cash Flows, Portfolios, and Asset Liability Management {20-30%} > > ### General Cash Flows, Portfolios, and Asset Liability Management > Understand key concepts concerning yield curves, rates of return, measures of duration and convexity, cash flow matching and immunization, and how to perform related calculations. > 1. Define and recognize the definitions of the following terms: [[Yield Rate]]/rate of return, [[Current Value]], [[Duration]] and [[Convexity]] ([[Macaulay]] and [[Modified]]), [[Portfolio]], [[Spot Rate]], [[Forward Rate]], [[Yield Curve]], [[Cash Flow]] and [[Duration Matching]], and [[immunization]] (including [[full immunization]] and [[Redington immunization]]). > 2. Calculate: > - The [[duration]] and **convexity** of a set of cash flows. > - Either **Macaulay** or **modified duration** given the other. > - The approximate change in present value due to a change in interest rate, > - Using [[1st-Order Linear Approximation]] based on modified duration. > - Using 1st-order approximation based on Macaulay duration. > - The present value of a set of cash flows, using a yield curve developed from forward and spot rates. > 3. Construct an investment portfolio to: > - Protect the value of an [[Asset-Liability Portfolio]] using either **Redington** or **full immunization** > - Exactly match a set of liability cash flows