Verified solution · Exam FM

SOA Exam FM Sample Question #310 Solution

This Exam FM sample reference tests Annuities. Split the repeating pattern into three perpetuities with three-year spacing. At 12.5%, the three-year rate is 42.3828%. Valuing the time-0, time-1, and time-2 sequences and solving the 9,450 price gives X = 2963.19, 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 Annuities question

Setup

Convert the annual rate to the effective three-year rate and split the repeating pattern by starting offset.

j=(1.125)^3-1

Model

Each offset stream is a three-year perpetuity-due, discounted by zero, one, or two years.

9450=\frac{1+j}{j}\left(100+Xv+100v^2\right)

Compute

With j = 0.42382813, solving the linear price equation gives X = 2963.194444.

X=2963.19444444

Answer

The middle payment is approximately 2,963, selecting choice B.

\boxed{X\approx2963\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 (2950) does not satisfy the sum of three offset three-year perpetuity-due streams; no distinct standard one-step error is identifiable.
CChoice C (3321) does not satisfy the sum of three offset three-year perpetuity-due streams; no distinct standard one-step error is identifiable.
DChoice D (3344) does not satisfy the sum of three offset three-year perpetuity-due streams; no distinct standard one-step error is identifiable.
EChoice E (3359) does not satisfy the sum of three offset three-year perpetuity-due streams; no distinct standard one-step error is identifiable.

Original practice · fully worked

Original variant: yield inferred from a repeating three-payment perpetuity pattern

A perpetuity-due repeats the annual payment pattern 50, 100, 150 forever. Its present value is 1732.37. Calculate the annual effective yield.

A
6.00%
B
6.30%
C
6.60%
D
6.90%
E
7.20%

Variant answer in brief

Writing one three-payment block over the repeating three-year discount denominator and solving the quoted price gives annual effective yield 6.00%, choice A.

Setup

Let v be the annual discount factor and value the first repeating block at times 0, 1, and 2.

PV_{\mathrm{block}}=50+100v+150v^2

Model

Repeat the block every three years as a geometric series.

1732.37=\frac{50+100v+150v^2}{1-v^3}

Compute

The positive yield root is 6.000000%.

i=v^{-1}-1=0.0600000000

Answer

The annual effective yield is 6.00%, selecting choice A.

\boxed{i=6.00\%\quad\text{(A)}}

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The 2210-page Financial Mathematics Proof Manual reorganizes 461 verified Exam FM solutions by syllabus skill and adds formula proofs, error patterns, and original worked practice.

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Cite this solution

ActuaryProof. “SOA Exam FM Sample Question #310 — Verified Solution.” Verified 2026-07-31.

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

How to solve this Annuities question

Setup

Model

Compute

Answer

All 461 Exam FM sample solutions in syllabus order

Why the other letters tempt

Original variant: yield inferred from a repeating three-payment perpetuity pattern

Variant answer in brief

Setup

Model

Compute

Answer

Related Exam FM solutions

Turn this solution into a complete study sequence

Cite this solution