[Exam FM Syllabus - October 2025](https://www.soa.org/49f424/globalassets/assets/files/edu/2025/fall/syllabi/2025-10-exam-fm-syllabus.pdf) | Learning Objective | Weight | | ----------------------------------------------------------------- | ------ | | 1. Time Value of Money | 5-15% | | 2. Annuities/Cash Flows with Non-Contingent Payments | 20-30% | | 3. Loans | 15-25% | | 4. Bonds | 15-25% | | 5. General Cash Flows, Portfolios, and Asset Liability Management | 20-30% | ## 1. Time Value of Money | Term | Definition | | ----------------------- | ---------------------------------------------------------------------- | | Time Value of Money | Present, future, and accumulated values across time. | | Interest rate | Rate charged or earned on principal. | | Simple interest | Linear growth over time: $A = P(1+it)$. | | Compound interest | Exponential growth over periods: $A = P(1+i)^n$. | | Accumulation function | Function describing growth of $1$ over time. | | Future value | Value of cash today at later date. | | Current value | Value at present moment, synonym for present value. | | Present value | Discounted value of future payment. | | Net present value (NPV) | PV of inflows – PV of outflows. | | Discount factor | Present worth of $1$ received later: $v = \frac{1}{1+i}$. | | Discount rate | Equivalent rate reducing value of future cash. | | Convertible m-thly | Nominal rate convertible $m$ times yearly. | | Nominal rate | Stated annual rate, not compounded. | | Effective rate | Annual rate reflecting compounding. | | Inflation rate | Percentage increase in price levels. | | Real interest rate | Adjusted for inflation: $(1+i) = (1+r)(1+\pi)$. | | Force of interest | Continuous compounding rate: $\delta = \lim_{m\to\infty} m\ln(1+i/m)$. | | Equation of value | Equality of PV of inflows and outflows. | ## 2. Annuities / Non-contingent Payments | Term | Definition | | ----------------------------------- | ------------------------------------------------- | | Annuities / Non-contingent Payments | PV, FV of regular non-contingent payments. | | Annuity-immediate | Payments at end of each period. | | Annuity-due | Payments at start of each period. | | Perpetuity | Infinite sequence of payments. | | Payable m-thly | Payments divided into $m$ installments annually. | | Continuously payable | Payments modeled as continuous cash flow. | | Level payment annuity | Equal payments each period. | | Arithmetic annuity | Payments increase or decrease linearly. | | Geometric annuity | Payments grow or shrink proportionally. | | Term of annuity | Duration until final payment. | | Level annuity finite term | Equal payments for limited time. | | Level perpetuity | Equal payments forever. | | Arithmetic progression finite term | Linearly changing payments, finite horizon. | | Arithmetic perpetuity | Linearly changing payments forever. | | Geometric progression finite term | Proportionally changing payments, finite horizon. | | Geometric perpetuity | Proportionally changing payments forever. | | Other non-level annuities | Any irregular structured payment streams. | ## 3. Loans | Term | Definition | | ------------------------- | ----------------------------------------------------- | | Loans | Understanding borrowing, payments, balances. | | Principal | Original loan amount borrowed. | | Interest | Payment for using borrowed funds. | | Term of loan | Duration of repayment. | | Outstanding balance | Remaining unpaid loan balance. | | Final payment | Lump sum payoff at end. | | Balloon payment | Large final repayment. | | Amortization | Schedule of principal and interest repayment. | | Solve loan variables | Find missing item from term, rate, amount, principal. | | Outstanding balance calc. | Value of loan owed at specific time. | | Split payment | Interest vs principal in each installment. | | Refinancing | New loan to replace old terms. | ## 4. Bonds | Term | Definition | | ------------------------ | ------------------------------------------- | | Bonds | Pricing and yield calculations for bonds. | | Price | Amount paid to buy bond. | | Book value | Accounting value of bond. | | Market value | Current trading value. | | Amortization of premium | Allocation of excess over par. | | Accumulation of discount | Growth of below-par purchase. | | Redemption value | Amount repaid at maturity. | | Par value | Face value of bond. | | Yield rate | Return earned from bond. | | Coupon | Regular bond payment. | | Coupon rate | Coupon as percent of par. | | Term of bond | Time until maturity. | | Callable bond | Issuer can redeem early. | | Non-callable bond | Cannot be redeemed early. | | Call price | Amount to redeem callable bond. | | Call premium | Excess over par when called. | | Reinvested coupons | Future value including reinvested payments. | | Solve bond values | Compute missing bond variables. | | Callable bond pricing | Ensure specified minimum yield. | ## 5. General Cash Flows, Portfolios, and Asset Liability Management | Term | Definition | | ----------------------------------------------- | ------------------------------------------------------------------------ | | General Cash Flows & Asset/Liability Management | Portfolio valuation, matching, and immunization. | | Yield rate / return | Profit rate from investment. | | Current value | Present worth of cash flows. | | Duration (Macaulay) | Time-weighted average of payments. | | Duration (Modified) | Sensitivity of price to interest rate. | | Convexity | Measure of curvature in price-yield relation. | | Portfolio | Collection of financial assets. | | Spot rate | Current yield for a single maturity. | | Forward rate | Implied future yield between maturities. | | Yield curve | Graph of yields vs maturities. | | Duration matching | Align durations of assets and liabilities. | | Immunization | Strategy to shield against interest changes. | | Redington immunization | Match value, duration, convexity conditions. | | Full immunization | Match exact liability timing with assets. | | Duration calculation | Compute time-weighted sensitivity. | | Convexity calculation | Compute second-order sensitivity. | | Duration conversion | Switch between Macaulay and modified. | | First-order PV change (mod. duration) | Approx. PV shift: ( \Delta PV \approx -D_{mod} \cdot PV \cdot \Delta i ) | | First-order PV change (Mac. duration) | PV shift using Macaulay duration. | | Yield curve PV | Present value using spot/forward rates. | | Construct immunized portfolio | Design assets to protect value under interest shifts. | | Exact cash flow match | Build portfolio to mirror liabilities exactly. |