Verified solution · Exam FM
This Exam FM sample reference tests Perpetuity Duration. At i = 10%, 1/d = 1.10/0.10 = 11 years. The result agrees with the published answer key, choice C.
Independent solution
Setup
For a unit perpetuity-immediate, price is the sum of vᵗ and the time-weighted numerator is the sum of tvᵗ.
Model
Dividing the two convergent geometric-series identities gives Macaulay duration 1/d, where d = i/(1 + i).
Compute
At i = 10%, 1/d = 1.10/0.10 = 11 years.
Answer
The calculation gives 11 years for perpetuity duration, matching published choice C.
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Error diagnosis
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Original practice · fully worked
An asset pays one unit at the end of every year forever. At an 8% annual effective rate, calculate its Macaulay duration.
The duration is 1.08/0.08 = 13.50 years. This selects choice D.
Setup
A unit perpetuity-immediate has Macaulay duration 1/d.
Model
At i = 8%, d = i/(1 + i) = 0.08/1.08.
Compute
The duration is 1.08/0.08 = 13.50 years.
Answer
The requested value is 13.5, so the correct choice is D.
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ActuaryProof. “SOA Exam FM Sample Question #31 — Verified Solution.” Verified 2026-07-31.
Source reference: official SOA sample-question PDF. Last reviewed 2026-07-31.
