Verified solution · Exam FM
This Exam FM sample reference tests Time-Varying Force of Interest. Year 5 runs from t = 4 to t = 5. Integrating 1/(t+8) over that interval gives log(13/12), so the annual accumulation is 13/12 and the effective rate is 8.333%, choice D.
Independent solution
Setup
The fifth year after time zero is the interval from t = 4 through t = 5.
Model
The antiderivative is the logarithm of t plus 8.
Compute
Exponentiating gives the one-year accumulation factor.
Answer
The effective rate in year 5 is 8.3%, choice D.
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Original practice · fully worked
A fund has force of interest delta of t equal to 0.02 plus 0.003t. Determine the effective return earned from time 1 through time 4.
The integrated force from time 1 to 4 is 0.0825. Exponentiating gives an effective return of 8.5999%, choice D.
Setup
An interval return is the exponential of integrated force.
Model
Integrate the constant and linear terms.
Compute
Convert log accumulation to effective return.
Answer
The three-year effective return is 8.60%, choice D.
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ActuaryProof. “SOA Exam FM Sample Question #324 — Verified Solution.” Verified 2026-07-31.
Source reference: official SOA sample-question PDF. Last reviewed 2026-07-31.
