Verified solution · Exam FM
This Exam FM sample reference tests Interest Rate Measures. Integrating the force gives accumulation a(t) = exp(0.03t + 0.0025t²). The time-0 deposit grows by a(2), and the time-1 deposit grows by a(2)/a(1). Their total is 211.07, so choice A is correct.
Independent solution
Setup
Integrate the linear force from time 0 to t.
Model
The first deposit uses accumulation a(2); the second uses the forward factor from time 1 to time 2.
Compute
The two contributions sum to 211.072018.
Answer
The account balance is approximately 211.07, selecting choice A.
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Original practice · fully worked
An account has force of interest δ(t) = 0.02 + 0.004t. A deposit of 100 is made at time 0 and a deposit of X at time 1. The balance at time 3 must be 250. Calculate X.
The time-0 deposit grows with a(3), while the time-1 deposit grows by a(3)/a(1). Solving the time-3 balance gives X = 134.16, choice E.
Setup
Integrate the force to obtain the time-0 accumulation function.
Model
Accumulate each deposit through its own holding interval to time 3.
Compute
Solving gives the time-1 deposit X = 134.16.
Answer
The required second deposit is 134.16, selecting choice E.
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ActuaryProof. “SOA Exam FM Sample Question #312 — Verified Solution.” Verified 2026-07-31.
Source reference: official SOA sample-question PDF. Last reviewed 2026-07-31.
