Worked solution · Exam FM
This Exam FM sample reference tests Duration and Convexity. The stated liability duration determines the five-year discount factor and yield; dividing 3.70 by one plus that yield gives modified duration 3.3057 years, choice B.
Independent solution
Setup
The immediate liability contributes value but zero to the duration numerator.
Model
Use the stated weighted time to solve for the five-year discount factor and hence the annual yield factor.
Compute
Convert Macaulay duration to modified duration by dividing by one plus yield.
Answer
The modified duration is approximately 3.31 years, corresponding to choice B.
Test the method on unseen problems
30 original general cash flows, portfolios, and asset liability management problems with complete solutions and wrong-choice analysis. Written for Exam FM, not copied from the SOA set. One-time $19 PDF.
Original practice · fully worked
A company owes 20,000 today and F in five years. At 5% effective annually, the combined Macaulay duration is 3.00 years. Determine F.
Target duration 3 requires the discounted future liability to equal 30,000, so F = 38,288.45, choice C.
Setup
The time-zero obligation enters the denominator but not the time-weighted numerator.
Model
Cross-multiply the target-duration equation to isolate the discounted future amount.
Compute
Its present value must be 30,000, which accumulates to 38,288.4469 in year five.
Answer
The future liability is 38,288.45, corresponding to choice C.
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These references share syllabus concepts or sit nearby in the official sequence. All 117 Exam FM general cash flows, portfolios, and asset liability management practice problems.
Drill the method: Exam FM Duration and Convexity problems
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