Actuarial Notes

Exam FM-2

The Financial Mathematics (FM-2) Exam is a 2.5 hour SOA 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.

Other resources

Learning Objectives

Time Value of Money (5–15%) 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.

Annuities/Cash Flows with Non-Contingent Payments (20–30%) Be able to calculate present value, current value, and accumulated value for sequences of 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.

Loans (15–25%) 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:

Bonds (15–25%) Understand key concepts concerning Bonds, and how to perform related calculations.

  1. Define and recognize the definitions of the following terms: 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/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
  1. Calculate the price of a callable bond to achieve a specified minimum yield

General Cash Flows, Portfolios, and Asset Liability Management (20–30%) 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:
  1. Construct an investment portfolio to:

Source Material

Source Material

  • Mathematics of Investment and Credit (Broverman, S.A. – 2024)
    • Chapters 1–7|
    • Candidates may also use the Seventh Edition (2017, ACTEX Learning, ISBN 978-1-63588-221-6), with the same sections
  • Mathematical Interest Theory (Vaaler, L.J.F., Harper, S.K., and Daniel, J.W. – 2019)
    • Chapters 1–6, 8–9|
  • Financial Mathematics: Theory and Practice (Brown, R. and Kopp, S. – 2024)
    • Chapter 1, all sections; Chapter 2, sections 1, 2, 3; Chapter 3, all sections; Chapter 4, sections 1, 3, 4, 5; Chapter 5, sections 1, 2, 3; Chapter 6, sections 1, 2, 3, 4, 5, 6; Chapter 7, sections 1, 2; Chapter 8, all sections; Chapter 9, all sections
    • Candidates may also use the First Edition (2012, ACTEX Learning, published by McGraw-Hill Ryerson, ISBN 978-1-63588-694-8), with the same chapters and sections
  • 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
  • Using Duration and Convexity to Approximate Change in Present Value (Alps - 2017)
    • Sections 1–4 (required reading)