Verified solution · Exam FM

SOA Exam FM Sample Question #174 Solution

This Exam FM sample reference tests Annuities and Perpetuities. The nine-unit annual increases have present value 2,500, leaving 100 of value for the level P perpetuity; therefore P/0.06 = 100 and P = 6, 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 and Perpetuities question

Setup

Decompose the payments into a level perpetuity of P and an arithmetic increase of nine per year.

2600=\frac{P}{0.06}+9v^9(Ia)_{\infty|\,0.06}

Model

The increasing component's discounted value is 2,500 under the stated timing and rate.

9v^9(Ia)_\infty=2500

Compute

Only 100 of the total price remains for the level perpetuity, so its annual payment is 100 times 0.06.

P/0.06=100

Answer

The first payment is 6.00, corresponding to choice B.

\boxed{P=6.00\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 is inconsistent with the level-plus-arithmetic perpetuity decomposition; no distinct standard single-step error producing it is identifiable.
CChoice C is inconsistent with the level-plus-arithmetic perpetuity decomposition; no distinct standard single-step error producing it is identifiable.
DChoice D is inconsistent with the level-plus-arithmetic perpetuity decomposition; no distinct standard single-step error producing it is identifiable.
EChoice E is inconsistent with the level-plus-arithmetic perpetuity decomposition; no distinct standard single-step error producing it is identifiable.

Original practice · fully worked

Original variant: first payment in an increasing civic stipend

A civic stipend pays P after one year and then increases by 5 each year forever. At 8% effective annually, the stream is worth 1,800. Determine P.

A
70.00
B
75.00
C
81.50
D
90.00
E
100.00

Variant answer in brief

Removing the five-unit arithmetic increase value leaves a level perpetuity with P = 81.50, choice C.

Setup

Write the annual payment as a level P plus an increment of five times year index minus one.

1800=\frac{P}{0.08}+\frac{5}{0.08^2}

Model

The delayed arithmetic increments have present value five divided by i squared.

\frac{P}{0.08}=1800-781.25=1018.75

Compute

After removing 781.25 from the total value, the level perpetuity component is 1,018.75.

P=81.50

Answer

Multiplying by 8% gives first payment 81.50, choice C.

\boxed{P=81.50\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 #174 — Verified Solution.” Verified 2026-07-31.

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

How to solve this Annuities and Perpetuities question

Setup

Model

Compute

Answer

All 461 Exam FM sample solutions in syllabus order

Why the other letters tempt

Original variant: first payment in an increasing civic stipend

Variant answer in brief

Setup

Model

Compute

Answer

Related Exam FM solutions

Turn this solution into a complete study sequence

Cite this solution