Verified solution · Exam FM

SOA Exam FM Sample Question #394 Solution

This Exam FM sample reference tests Interest Rate Valuation. Accumulation during the fifth year is the exponential of the force integrated from time 4 to 5; the integral is ln(13/12), giving effective rate 8.33%, choice D.

Independent analysis by ActuaryProof · reviewed August 4, 2026

Official wording withheld. Read the problem in the official SOA sample-question PDF. This page provides only our independently written analysis.

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Independent solution

How to solve this Interest Rate Valuation question

Setup

The fifth year is the interval from time four through time five.

1+i_5=\exp\left(\int_4^5\frac{dt}{t+8}\right)

Model

Integrate the time-varying force over exactly that interval.

\int_4^5\frac{dt}{t+8}=\ln(13)-\ln(12)=\ln(13/12)

Compute

Exponentiating the log ratio gives accumulation factor 13/12.

1+i_5=\frac{13}{12}

Answer

The effective fifth-year rate is 8.33%, corresponding to choice D.

\boxed{i_5=8.33\%\quad\text{(D)}}

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Error diagnosis

Why the other letters tempt

These notes identify the calculation error associated with each wrong letter when that error is reproducible.

AChoice A is inconsistent with the force integral over times four through five; no distinct standard single-step error producing it is identifiable.
BChoice B is inconsistent with the force integral over times four through five; no distinct standard single-step error producing it is identifiable.
CChoice C is inconsistent with the force integral over times four through five; no distinct standard single-step error producing it is identifiable.
EChoice E is inconsistent with the force integral over times four through five; no distinct standard single-step error producing it is identifiable.

Original practice · fully worked

Original variant: multi-year accumulation under a varying force

The force of interest at time t is one divided by t plus 6. Determine the effective accumulation rate over the two-year interval from time 2 to time 4.

A
15.0%
B
20.0%
C
25.0%
D
30.0%
E
35.0%

Variant answer in brief

Integrating from 2 to 4 gives log of 10/8, so the two-year accumulation factor is 1.25 and the effective interval rate is 25%, choice C.

Setup

Use the full two-year interval rather than an annualized average force.

1+i_{[2,4]}=\exp\left(\int_2^4\frac{dt}{t+6}\right)

Model

The antiderivative is the logarithm of t plus six.

\int_2^4\frac{dt}{t+6}=\ln(10/8)

Compute

Exponentiation converts the log difference to endpoint ratio 10/8.

1+i_{[2,4]}=10/8=1.25

Answer

The effective rate over the interval is 25.0%, corresponding to choice C.

\boxed{i_{[2,4]}=25.0\%\quad\text{(C)}}

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Cite this solution

ActuaryProof. “SOA Exam FM Sample Question #394 — Verified Solution.” Verified 2026-07-31.

Source reference: official SOA sample-question PDF. Last reviewed 2026-07-31.

How to solve this Interest Rate Valuation question

Setup

Model

Compute

Answer

All 461 Exam FM sample solutions in syllabus order

Why the other letters tempt

Original variant: multi-year accumulation under a varying force

Variant answer in brief

Setup

Model

Compute

Answer

Related Exam FM solutions

Turn this solution into a complete study sequence

Cite this solution