Verified solution · Exam FM

SOA Exam FM Sample Question #24 Solution

This Exam FM sample reference tests Perpetuities at Different Frequencies. Substitution in q/(1 − q) gives 32.599. The requested value is 32.6. 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 Perpetuities at Different Frequencies question

Setup

Let v be the annual discount factor. The first perpetuity pays every three years, so its geometric ratio is v³.

32=\frac{10v^3}{1-v^3}\Longrightarrow v^3=\frac{32}{42}

Model

Its quoted value gives 32 = 10v³/(1 − v³), hence v³ = 32/42. The second stream’s payment interval is obtained by taking the corresponding root of v before applying the perpetuity formula.

X=\frac{v^{1/3}}{1-v^{1/3}}

Compute

Substitution in q/(1 − q) gives 32.599. The requested value is 32.6.

X=32.599

Answer

The calculation gives 32.6 for perpetuities at different frequencies, matching published choice B.

\boxed{X=32.6\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 (31.6) does not match the checked perpetuities at different frequencies result (32.6); no distinct standard one-step error is identifiable.
CChoice C (33.6) does not match the checked perpetuities at different frequencies result (32.6); no distinct standard one-step error is identifiable.
DChoice D (34.6) does not match the checked perpetuities at different frequencies result (32.6); no distinct standard one-step error is identifiable.
EChoice E (35.6) does not match the checked perpetuities at different frequencies result (32.6); no distinct standard one-step error is identifiable.

Original practice · fully worked

Original variant: quarterly perpetuity from a biennial quote

A perpetuity paying 20 every two years has present value 100. At the same annual rate, find the value of a perpetuity paying 1 every quarter.

A
40.00
B
42.00
C
43.38
D
45.00
E
50.00

Variant answer in brief

The quarterly perpetuity is worth 43.3804, or 43.38. This selects choice C.

Setup

The two-year perpetuity price gives v² = 5/6.

100=\frac{20v^2}{1-v^2}\Longrightarrow v^2=\frac56

Model

A quarterly payment interval uses q = v to the power 1/4; apply the unit perpetuity formula q/(1 − q).

q=v^{1/4}=(5/6)^{1/8}

Compute

The quarterly perpetuity is worth 43.3804, or 43.38.

PV=\frac q{1-q}=43.3804

Answer

The requested value is 43.38, so the correct choice is C.

\boxed{PV=43.38\quad\text{(C)}}

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Cite this solution

ActuaryProof. “SOA Exam FM Sample Question #24 — Verified Solution.” Verified 2026-07-31.

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

How to solve this Perpetuities at Different Frequencies question

Setup

Model

Compute

Answer

All 461 Exam FM sample solutions in syllabus order

Why the other letters tempt

Original variant: quarterly perpetuity from a biennial quote

Variant answer in brief

Setup

Model

Compute

Answer

Related Exam FM solutions

Turn this solution into a complete study sequence

Cite this solution