Verified solution · Exam FM
This Exam FM sample reference tests Immunization and Asset-Liability Management. The liabilities have present value 1153.84 and duration 2.4278. Matching those with year-1 and year-3 asset payments gives X = 346.61 and Y = 953.57, so Y/X = 2.75 and choice B.
Independent solution
Setup
Compute the liability present value and time-weighted present value at 5%.
Model
Match both quantities with the asset payments at years 1 and 3.
Compute
Solving gives X = 346.6148, Y = 953.5714, and ratio 2.751098.
Answer
The required payment ratio is approximately 2.75, selecting choice B.
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Error diagnosis
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Original practice · fully worked
At a 5% annual yield, assets pay 600 at year 1 and 800 at year 4. Liabilities pay 500 at year 2 and 900 at year 3. Calculate asset Macaulay duration minus liability Macaulay duration.
The asset and liability durations are 2.6058 and 2.6316 years. Their difference is -0.0258 years, choice A.
Setup
Discount each asset and liability payment at 5% and retain its payment time.
Model
The duration mismatch is asset duration minus liability duration.
Compute
The two durations are 2.605808 and 2.631579, giving mismatch -0.025771 years.
Answer
The duration mismatch is -0.0258 years, selecting choice A.
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These references share syllabus concepts or sit nearby in the official sequence. All 118 Exam FM general cash flows, portfolios, and asset liability management practice problems.
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ActuaryProof. “SOA Exam FM Sample Question #249 — Verified Solution.” Verified 2026-07-31.
Source reference: official SOA sample-question PDF. Last reviewed 2026-07-31.
