Verified solution · Exam FM

SOA Exam FM Sample Question #186 Solution

This Exam FM sample reference tests Interest Rate Valuation. One quarter contains three monthly payment periods, so the monthly effective factor is the cube root of 1.02; the matching expression is choice A.

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

Convert the nominal quarterly quote to its effective rate for one quarter.

1+i_q=1+\frac{0.08}{4}=1.02

Model

A quarter comprises three monthly payment periods, so three monthly accumulation factors must equal the quarterly factor.

(1+i_m)^3=1.02

Compute

Taking the positive cube root isolates the monthly effective rate.

i_m=(1.02)^{1/3}-1

Answer

The equivalent rate per monthly payment period is the expression in choice A.

\boxed{i_m=(1+0.08/4)^{1/3}-1\quad\text{(A)}}

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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.

BDividing the nominal annual quote by 12 ignores that the quoted conversion frequency is quarterly.
CThis compounds a nominal-twelfth rate for a quarter even though no monthly nominal quote was given.
DThis treats a nominal monthly fraction as though it accumulated for a full year.
EThis computes the annual effective rate from quarterly compounding, not the effective rate per month.

Original practice · fully worked

Original variant: convert a semiannual quote to a monthly rate

A savings contract credits 9% nominal interest convertible semiannually, while deposits arrive monthly. Determine the monthly effective rate equivalent to the quoted accumulation.

A
0.6250%
B
0.7000%
C
0.7363%
D
0.7500%
E
1.5000%

Variant answer in brief

Six monthly factors must reproduce the 4.5% half-year factor, giving a monthly effective rate of 0.7363%, choice C.

Setup

The nominal quote supplies a 4.5% effective rate over each six-month conversion period.

(1+i_m)^6=1+\frac{0.09}{2}=1.045

Model

Equate that half-year factor to six identical monthly accumulation factors.

i_m=(1.045)^{1/6}-1

Compute

The sixth root gives monthly rate 0.00736312.

i_m=0.00736312

Answer

The equivalent monthly effective rate is 0.7363%, corresponding to choice C.

\boxed{i_m=0.7363\%\quad\text{(C)}}

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ActuaryProof. “SOA Exam FM Sample Question #186 — 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: convert a semiannual quote to a monthly rate

Variant answer in brief

Setup

Model

Compute

Answer

Related Exam FM solutions

Turn this solution into a complete study sequence

Cite this solution