Verified solution · Exam FM

SOA Exam FM Sample Question #424 Solution

This Exam FM sample reference tests Geometric Perpetuities. The mistaken first payment identifies the unchanged contract price as 1500 divided by 0.107. Using the correct denominator 0.098 gives a first payment of 1373.83, choice D.

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 Geometric Perpetuities question

Setup

Let P be the sale price and let r = -0.02 be the annual payment growth rate.

P=\frac{K}{i-r}=\frac{K}{i+0.02}

Model

The mistaken calculation used an 8.7% yield and first payment 1500, which determines the price the company intended to charge.

P=\frac{1{,}500}{0.087+0.02}

Compute

Keep that price fixed and replace the mistaken yield with 7.8%.

K=P(0.078+0.02)

K=1{,}500\frac{0.098}{0.107}=1{,}373.832

Answer

The corrected first payment rounds to 1374, choice D.

\boxed{K\approx1{,}374\quad\text{(D)}}

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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 applies the ratio of discount factors in the reverse direction and reduces the payment too far.
BChoice B adjusts 1500 by the relative change in yield alone, ignoring the additional 2% decline term.
CChoice C uses 7.8% divided by 8.7% even though a geometric perpetuity is priced with i minus r.
EChoice E uses 9.8% over 10.6%; the mistaken denominator is 10.7%, not 10.6%.

Original practice · fully worked

Original variant: infer the payment growth rate

A scholarship fund is priced at 5,000 and pays 250 one year from now. Subsequent annual payments grow at a constant rate g forever. The annual effective yield is 6%. Determine g.

A
−1.0%
B
0.0%
C
1.0%
D
2.0%
E
5.0%

Variant answer in brief

The geometric-perpetuity equation gives 5000 = 250 divided by 0.06 minus g. Solving yields g = 1.0%, choice C.

Setup

The first scholarship payment is one year away, so use the perpetuity-immediate formula.

P=\frac{K_1}{i-g}

Model

Insert the quoted price, first payment, and yield.

5{,}000=\frac{250}{0.06-g}

Compute

Invert the equation and isolate the growth rate.

0.06-g=\frac{250}{5{,}000}=0.05

g=0.01

Answer

Annual payments grow by 1.0%, choice C.

\boxed{g=1.0\%\quad\text{(C)}}

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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 #424 — Verified Solution.” Verified 2026-07-31.

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

How to solve this Geometric Perpetuities question

Setup

Model

Compute

Answer

All 461 Exam FM sample solutions in syllabus order

Why the other letters tempt

Original variant: infer the payment growth rate

Variant answer in brief

Setup

Model

Compute

Answer

Related Exam FM solutions

Turn this solution into a complete study sequence

Cite this solution