Exam FM technique guide
Learn how to recognize the method, recall the formulas that control it, and work through 43 sample-question solutions.
Try this original problem before opening the solution. Then compare the method with SOA Exam FM sample question 135.
Original practice · fully worked
A transit note pays 60 annually. It may be redeemed for 1,050 after year 5, for 1,020 after year 10, or for 1,000 at maturity in year 15. At a required 5% annual yield, which date produces the lowest acceptable purchase price?
The endpoint prices are 1,082.47, 1,089.50, and 1,103.80; year 5 is smallest, choice A.
Setup
Each possible redemption creates a different complete cash-flow stream from purchase through that date.
Model
Price each stream at 5%, including all coupons up to the relevant redemption.
Compute
The three values increase from 1,082.47 to 1,089.50 to 1,103.80.
Answer
The earliest redemption limits the guaranteed price, so year 5 and choice A are correct.
Calculator reproduction
Technique orientation
A bond price is the present value of coupons and redemption proceeds at the investor’s yield. The coupon rate creates the cash flows; the yield rate values them. Keeping those roles separate turns most premium, discount, book-value, and callable-bond questions into ordinary dated cash-flow calculations.
Exam FM frequently quotes annual coupon and yield rates while coupons are paid more often. Convert both to the coupon period, count the remaining coupons, and put redemption at the final applicable date. For callable bonds, value every allowed redemption scenario needed to protect the purchaser’s stated yield rather than assuming maturity is decisive.
Recognition audit
Before calculation
Name the requested quantity, mark its units or time point, and identify the assumption that permits the formula. Only then insert the numerical inputs. This separates model errors from arithmetic errors and makes the answer-choice comparison auditable.
Formula core
These identities are starting points, not substitutes for checking support, timing, rate periods, or independence assumptions.
Coupon-bond price
Fr is the coupon per period and C is the redemption value; i is the yield per coupon period.
Premium-discount decomposition
Price exceeds redemption when the coupon per period exceeds interest on the redemption value at the yield rate.
Book-value recursion
Accrue the current book value at the yield, then remove the coupon paid at period end.
Three failure modes to catch
Verified practice ledger
The list is grouped by current official syllabus area. Every link opens a step-labeled solution, verification artifact, distractor analysis, and one fully worked original variant.
43 verified references
Continue the study loop
The complete Exam FM manual includes all active sample-reference solutions, their wrong-choice analysis, and one independently written worked variant per reference. The free formula sheet is the compact companion for recall between practice sessions.
Related drills
Switch techniques when you can identify the current method before writing a formula and can explain each wrong-choice mechanism.
28 verified problems
Constant and variable force of interest, effective and nominal rate conversions, accumulation integrals, and 28 verified Exam FM solutions.
54 verified problems
Level, due, deferred, increasing, growing, and perpetual payment streams under consistent timing and rates.
48 verified problems
Level-payment loans, prospective and retrospective balances, principal-interest splits, refinancing, and balloon payments.
31 verified problems
Macaulay and modified duration, convexity, price sensitivity, immunization, and portfolio weighting.
