Verified solution · Exam FM
This Exam FM sample reference tests Equivalent Discount Rate over Mixed Interest Regimes. The loan grows for two years at 5% and then by the force integral from time 2 to 5, producing 220.50. The constant annual discount rate satisfying 100 = 220.50 times one minus d to the fifth is 14.627%, choice C.
Independent solution
Setup
Accumulate the principal through the first two effective-rate years.
Model
Integrate the later force from time 2 through time 5.
Compute
The terminal amount is 220.50. Define a constant annual effective discount over all five years.
Answer
Solving gives 14.627%, choice C.
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Original practice · fully worked
A deposit of 200 earns 4% effective during its first year. From time 1 to time 3, its force of interest is 0.02t. Determine the value at time 3.
After the first year the deposit is 208. The later integrated force is 0.08, so the time-3 value is 225.32, choice C.
Setup
Accumulate the first year under the effective rate.
Model
Integrate the linear force over times 1 through 3.
Compute
Apply the exponential accumulation to the year-1 balance.
Answer
The terminal value is 225.32, choice C.
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ActuaryProof. “SOA Exam FM Sample Question #365 — Verified Solution.” Verified 2026-07-31.
Source reference: official SOA sample-question PDF. Last reviewed 2026-07-31.
