Verified solution · Exam FM
This Exam FM sample reference tests Full Immunization with Zero-Coupon Assets. At the liability date, the five-year zero contributes 388888 of value and the other zero contributes 1361112. The first-derivative condition makes its timing displacement two years, so its maturity is year 14, choice B.
Independent solution
Setup
Move all values to the liability date at year 12. Let N be the maturity value of the n-year zero.
Model
Full immunization also sets the first timing moment about year 12 to zero.
Compute
The first equation assigns 1361112 of year-12 value to the later zero. Substitute it into the moment equation.
Answer
The second zero matures in year 14, choice B.
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Error diagnosis
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Original practice · fully worked
A liability has present value 500,000 and Macaulay duration 10 years. It is fully immunized at a 6% annual yield with zero-coupon assets maturing in 6 and 14 years. Determine the maturity value of the 14-year zero.
Duration 10 is midway between 6 and 14, so each zero receives 250000 of present value. Accumulating the long allocation for 14 years gives maturity value 565225.99, choice D.
Setup
Let w be the present-value share in the 14-year zero.
Model
The duration equation gives equal present-value shares.
Compute
Convert the time-zero allocation to its year-14 maturity amount.
Answer
The long zero matures for about 565226, choice D.
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ActuaryProof. “SOA Exam FM Sample Question #339 — Verified Solution.” Verified 2026-07-31.
Source reference: official SOA sample-question PDF. Last reviewed 2026-07-31.
