Verified solution · Exam FM
This Exam FM sample reference tests Force of Interest. The year 2024 corresponds to t from 4 to 5. Integrating 1 divided by 20 plus t gives log of 25 divided by 24, so the annual accumulation is 25/24 and the effective rate is 4.1667%, choice C.
Independent solution
Setup
Measure the requested calendar year from the stated January 2020 origin.
Model
An accumulation factor under a time-varying force is the exponential of its integral.
Compute
Integrate the logarithmic derivative and exponentiate.
Answer
The equivalent annual effective rate is 4.17%, choice C.
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Original practice · fully worked
A fund has force of interest delta of t equal to 0.03 plus 0.002t, where t is measured in years. Determine the effective return earned from time 2 through time 5.
The integrated force from 2 to 5 is 0.111. Exponentiating gives an effective three-year return of 11.7395%, choice D.
Setup
The return over an interval is determined by the integral of the force, not by a single endpoint value.
Model
Integrate the constant and linear parts over the three-year interval.
Compute
Convert log accumulation to effective accumulation.
Answer
The effective return is 11.74%, choice D.
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ActuaryProof. “SOA Exam FM Sample Question #442 — Verified Solution.” Verified 2026-07-31.
Source reference: official SOA sample-question PDF. Last reviewed 2026-07-31.
