Verified solution · Exam FM
This Exam FM sample reference tests Immunization and Asset-Liability Management. The time-4 asset of 250,000 directly matches that portion of the liability, leaving 500,000. Matching value and first derivative with the year-2 and year-5 assets gives three times AX times v to the −2 equal to 500,000, so AX = 150416.67, choice A.
Independent solution
Setup
Apply the time-4 asset directly against the liability, leaving 500,000 to immunize with the outer cash flows.
Model
At time 4, match value and the first sensitivity of the year-2 and year-5 cash flows.
Compute
Eliminating AZ gives 500,000 = 3AXv to the −2, so AX = 150416.666667.
Answer
Asset X pays approximately 150,000, selecting choice A.
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Original practice · fully worked
A liability of 600,000 is due at year 4. Assets pay 100,000 at year 2, 226056.13 at year 5, and Y at year 4. The annual discount factor is 0.96, and the two outer assets are already chosen so their duration effects around year 4 cancel. Calculate Y for full value matching.
At year 4, the early asset accumulates two periods and the late asset discounts one period. Subtracting those outer values from 600,000 leaves central payment 274,479.17, choice C.
Setup
Use year 4 as the comparison date and move each outer cash flow to that date with v = 0.96.
Model
The supplied outer face amounts satisfy the zero first-moment condition around year 4.
Compute
Subtracting the outer time-4 values gives Y = 274479.17.
Answer
The central asset must pay 274,479.17, selecting choice C.
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ActuaryProof. “SOA Exam FM Sample Question #304 — Verified Solution.” Verified 2026-07-31.
Source reference: official SOA sample-question PDF. Last reviewed 2026-07-31.
