Verified solution · Exam FM
This Exam FM sample reference tests Immunization and Asset-Liability Management. Matching duration 3 with one- and four-year zeros requires the four-year present value to be twice the one-year present value. The face amounts then imply the annual accumulation factor cubed is 1.25. Matching present values and accumulating to year 3 gives liability 69623.83, choice C.
Independent solution
Setup
A single year-3 liability has duration 3, so impose that duration on the two zero-coupon assets.
Model
Insert the face amounts to recover the flat annual accumulation factor.
Compute
The annual yield is 7.721735%. Asset present value is 55699.07, which accumulates to liability 69623.83 at year 3.
Answer
The liability amount is approximately 69,624, selecting choice C.
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Original practice · fully worked
A one-year zero-coupon bond has face 20,000 and a five-year zero has face 60,000. Under a flat annual yield, the two-bond portfolio must have Macaulay duration 3 years. Calculate the annual effective yield.
Duration 3 requires equal present values in the one- and five-year positions. Equating their discounted faces gives the fourth power of 1 + i equal to 3, so yield 31.61%, choice E.
Setup
A duration midway between years 1 and 5 requires equal market-value weights.
Model
Equate the discounted face amounts under the flat yield.
Compute
Thus the fourth power of 1 + i is 3, giving yield 31.607401%.
Answer
The annual effective yield is 31.61%, selecting choice E.
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ActuaryProof. “SOA Exam FM Sample Question #275 — Verified Solution.” Verified 2026-07-31.
Source reference: official SOA sample-question PDF. Last reviewed 2026-07-31.
