Verified solution · Exam FM

SOA Exam FM Sample Question #411 Solution

This Exam FM sample reference tests Duration and Convexity. For a level perpetuity-immediate, modified duration equals one divided by yield; duration 15 gives i = 1/15, and Macaulay duration is 15(1 + i) = 16, choice E.

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

Use the price derivative of a level perpetuity-immediate to relate modified duration and yield.

D_{\mathrm{mod}}=\frac{1}{i}=15

Model

The observed modified duration fixes the annual yield at one fifteenth.

i=\frac{1}{15}

Compute

Convert to Macaulay duration by multiplying by one plus yield.

D_M=(1+i)D_{\mathrm{mod}}=15\left(1+\frac1{15}\right)=16

Answer

The Macaulay duration is 16.00 years, corresponding to choice E.

\boxed{D_M=16.00\quad\text{(E)}}

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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 level-perpetuity duration identities; no distinct standard single-step error producing it is identifiable.
BChoice B is inconsistent with the level-perpetuity duration identities; no distinct standard single-step error producing it is identifiable.
CChoice C is inconsistent with the level-perpetuity duration identities; no distinct standard single-step error producing it is identifiable.
DChoice D is inconsistent with the level-perpetuity duration identities; no distinct standard single-step error producing it is identifiable.

Original practice · fully worked

Original variant: yield inferred from perpetuity modified duration

A level annual perpetuity-immediate has modified duration 8 years. Determine its annual effective yield.

A
10.5%
B
11.5%
C
12.5%
D
13.5%
E
14.5%

Variant answer in brief

Modified duration of a level perpetuity is one divided by yield, so the yield is 12.5%, choice C.

Setup

Write the modified-duration identity for a level perpetuity-immediate.

8=\frac1i

Model

Invert the observed eight-year measure.

8i=1

Compute

The resulting annual rate is 0.125.

i=0.125

Answer

The annual effective yield is 12.5%, corresponding to choice C.

\boxed{i=12.5\%\quad\text{(C)}}

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ActuaryProof. “SOA Exam FM Sample Question #411 — 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 inferred from perpetuity modified duration

Variant answer in brief

Setup

Model

Compute

Answer

Related Exam FM solutions

Turn this solution into a complete study sequence

Cite this solution