Verified solution · Exam FM

SOA Exam FM Sample Question #375 Solution

This Exam FM sample reference tests Duration and Convexity. Modified duration 5.76 must pair with Macaulay duration 6, giving one plus yield 6/5.76; applying the same factor to Macaulay duration 5 gives modified duration 4.800, choice B.

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 Duration and Convexity question

Setup

At a positive yield, modified duration is smaller than its corresponding Macaulay duration.

D_{\mathrm{mod}}=\frac{D_M}{1+r}

Model

Therefore 5.76 pairs with the six-year Macaulay measure and identifies the common yield factor.

1+r=\frac{6}{5.76}=1.0416667

Compute

Divide the other five-year Macaulay duration by that same factor.

d=\frac{5}{1.0416667}=4.800

Answer

The remaining modified duration is 4.800 years, corresponding to choice B.

\boxed{d=4.800\quad\text{(B)}}

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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 common Macaulay-to-modified duration factor; no distinct standard single-step error producing it is identifiable.
CChoice C is inconsistent with the common Macaulay-to-modified duration factor; no distinct standard single-step error producing it is identifiable.
DChoice D is inconsistent with the common Macaulay-to-modified duration factor; no distinct standard single-step error producing it is identifiable.
EChoice E is inconsistent with the common Macaulay-to-modified duration factor; no distinct standard single-step error producing it is identifiable.

Original practice · fully worked

Original variant: yield recovered from paired duration measures

A municipal bond has Macaulay duration 6.00 years and modified duration 5.70 years. Determine its annual effective yield.

A
3.26%
B
4.26%
C
5.26%
D
6.26%
E
7.26%

Variant answer in brief

The ratio of Macaulay to modified duration is 1.05263, giving annual yield 5.26%, choice C.

Setup

Use the annual effective conversion between the two duration measures.

6.00=(1+i)(5.70)

Model

Their ratio equals one plus the bond yield.

1+i=\frac{6.00}{5.70}=1.0526316

Compute

Subtracting one from 1.0526316 gives 0.0526316.

i=0.0526316

Answer

The annual effective yield is 5.26%, corresponding to choice C.

\boxed{i=5.26\%\quad\text{(C)}}

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ActuaryProof. “SOA Exam FM Sample Question #375 — Verified Solution.” Verified 2026-07-31.

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

How to solve this Duration and Convexity question

Setup

Model

Compute

Answer

All 461 Exam FM sample solutions in syllabus order

Why the other letters tempt

Original variant: yield recovered from paired duration measures

Variant answer in brief

Setup

Model

Compute

Answer

Related Exam FM solutions

Turn this solution into a complete study sequence

Cite this solution