Verified solution · Exam FM
This Exam FM sample reference tests Duration and Convexity. The zero's modified duration gives yield 7.991%; at that yield the ten level payments have a present-value-weighted mean time of 4.872 years, choice D.
Independent solution
Setup
A ten-year zero has Macaulay duration ten, so its modified duration identifies the yield.
Model
Use that yield to discount the ten annual annuity payments.
Compute
The ratio of the time-weighted sum to the ordinary present-value sum is 4.87195.
Answer
The annuity Macaulay duration is 4.87 years, corresponding to choice D.
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Original practice · fully worked
An eight-year zero-coupon security has modified duration 7.40 years. Determine its annual effective yield.
An eight-year zero has Macaulay duration 8, so 8/7.40 minus one gives yield 8.11%, choice C.
Setup
The only payment occurs in year eight, making Macaulay duration exactly eight.
Model
Convert that Macaulay duration to the observed modified duration.
Compute
Solving the one-step equation gives 0.0810811.
Answer
The annual effective yield is 8.11%, corresponding to choice C.
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ActuaryProof. “SOA Exam FM Sample Question #376 — Verified Solution.” Verified 2026-07-31.
Source reference: official SOA sample-question PDF. Last reviewed 2026-07-31.
