Verified solution · Exam FM
This Exam FM sample reference tests Interest Rate Measures. The force integrates to t²/100, so 300 grows by e to year 10 and the time-4 deposit grows by e to the 0.84. Setting total earned interest equal to 4X gives X = 192.08, choice D.
Independent solution
Setup
Integrate the force from zero to time t to obtain the fund's accumulation function.
Model
The first deposit grows from time 0 to 10, while X grows only from time 4 to 10.
Compute
Total interest is terminal value minus deposits. Solving that amount equal to 4X gives 192.084590.
Answer
The time-4 deposit is approximately 192, selecting choice D.
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Original practice · fully worked
A fund has force of interest δ(t) = a t. One unit invested at time 1 grows to 1.50 at time 5. Calculate a.
The integrated force from time 1 to 5 is 12a. Equating its exponential to 1.50 gives a = 0.033789, choice B.
Setup
Integrate the linear force only over the actual investment interval.
Model
Set the exponential accumulation equal to the observed growth factor.
Compute
Taking logarithms gives a = 0.03378876.
Answer
The force coefficient is 0.033789, selecting choice B.
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ActuaryProof. “SOA Exam FM Sample Question #303 — Verified Solution.” Verified 2026-07-31.
Source reference: official SOA sample-question PDF. Last reviewed 2026-07-31.
