Verified solution · Exam FM
This Exam FM sample reference tests Duration and Convexity. A perpetuity-immediate has Macaulay duration 1 + 1/i; duration 17.6 implies i = 1/16.6, and at rate 2i the duration becomes 1 + 16.6/2 = 9.3, choice B.
Independent solution
Setup
For an end-of-year level perpetuity, duration has the closed form one plus the reciprocal of yield.
Model
The original duration therefore determines the reciprocal yield as 16.6.
Compute
Doubling the yield halves that reciprocal component but leaves the leading one unchanged.
Answer
The new Macaulay duration is 9.3 years, which is choice B.
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Error diagnosis
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Original practice · fully worked
A perpetual public-radio grant pays at each year-end and has Macaulay duration 21 years at yield i. If the yield becomes 1.5i, calculate the new Macaulay duration.
Duration 21 implies i = 5%; at 7.5%, perpetuity duration is 14.33, choice C.
Setup
Use the end-of-year perpetuity duration formula to recover the original yield.
Model
The duration of 21 means the reciprocal-yield component is 20, hence i is 5%.
Compute
At one and a half times that rate, the new yield is 7.5% and duration is 14.3333.
Answer
The revised duration is 14.33 years, choice C.
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Drill the method: Exam FM Duration and Convexity problems
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ActuaryProof. “SOA Exam FM Sample Question #144 — Verified Solution.” Verified 2026-07-31.
Source reference: official SOA sample-question PDF. Last reviewed 2026-07-31.
