Verified solution · Exam FM

SOA Exam FM Sample Question #32 Solution

This Exam FM sample reference tests Growing Perpetuity Duration. Using i = 5% and g = 2% gives 1.05/0.03 = 35 years. The result agrees with the published answer key, 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 Growing Perpetuity Duration question

Setup

Discounted payments in the growing perpetuity form a geometric sequence with ratio q = 1.02/1.05. Treat q as the discount factor for an equivalent level perpetuity.

q=\frac{1.02}{1.05}=\frac1{1+j}

Model

The weighted-average payment time is therefore the level-perpetuity duration under the net rate, equal to (1 + i)/(i − g).

D_M=\frac1{d_j}=\frac{1+j}{j}

Compute

Using i = 5% and g = 2% gives 1.05/0.03 = 35 years.

D_M=\frac{1.05}{0.05-0.02}=35

Answer

The calculation gives 35 for growing perpetuity duration, matching published choice B.

\boxed{D_M=35\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 (27) does not match the checked growing perpetuity duration result (35); no distinct standard one-step error is identifiable.
CChoice C (44) does not match the checked growing perpetuity duration result (35); no distinct standard one-step error is identifiable.
DChoice D (52) does not match the checked growing perpetuity duration result (35); no distinct standard one-step error is identifiable.
EChoice E (58) does not match the checked growing perpetuity duration result (35); no distinct standard one-step error is identifiable.

Original practice · fully worked

Original variant: duration of growing dividends

Dividends are paid annually forever and grow 2% each year. At a 6% annual effective valuation rate, find the Macaulay duration.

A
24.0
B
25.0
C
26.5
D
28.0
E
30.0

Variant answer in brief

The duration is 1.06/0.04 = 26.50 years. This selects choice C.

Setup

For growth g below yield i, growing-perpetuity duration is (1 + i)/(i − g).

D_M=\frac{1+i}{i-g}

Model

Insert annual yield 6% and growth 2%.

i=0.06,\quad g=0.02

Compute

The duration is 1.06/0.04 = 26.50 years.

D_M=1.06/0.04=26.5

Answer

The requested value is 26.5, so the correct choice is C.

\boxed{D_M=26.50\quad\text{(C)}}

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Cite this solution

ActuaryProof. “SOA Exam FM Sample Question #32 — Verified Solution.” Verified 2026-07-31.

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

How to solve this Growing Perpetuity Duration question

Setup

Model

Compute

Answer

All 461 Exam FM sample solutions in syllabus order

Why the other letters tempt

Original variant: duration of growing dividends

Variant answer in brief

Setup

Model

Compute

Answer

Related Exam FM solutions

Turn this solution into a complete study sequence

Cite this solution