Verified solution · Exam FM

SOA Exam FM Sample Question #173 Solution

This Exam FM sample reference tests Annuities and Perpetuities. The effective rate per three-year payment period is 22.5043%; the perpetuity-due factor is 5.443595, so X = 735/5.443595 = 135.02, choice A.

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

Payments occur every three years beginning immediately, so use a three-year effective rate and a perpetuity-due.

j=(1.07)^3-1=0.225043

Model

Convert 7% annual effective to the three-year rate before applying the due perpetuity factor.

735=X\ddot a_{\infty|\,j}=X\frac{1+j}{j}

Compute

The factor is 5.443595, yielding payment 135.02.

X=735/5.443595=135.02

Answer

The payment at each three-year boundary is about 135, choice A.

\boxed{X\approx135\quad\text{(A)}}

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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.

BChoice B is inconsistent with the three-year-rate perpetuity-due factor; no distinct standard single-step error producing it is identifiable.
CChoice C is inconsistent with the three-year-rate perpetuity-due factor; no distinct standard single-step error producing it is identifiable.
DChoice D is inconsistent with the three-year-rate perpetuity-due factor; no distinct standard single-step error producing it is identifiable.
EChoice E is inconsistent with the three-year-rate perpetuity-due factor; no distinct standard single-step error producing it is identifiable.

Original practice · fully worked

Original variant: quadrennial heritage grants

A heritage fund pays X immediately and every four years thereafter forever. At 5% effective annually, the fund is worth 1,000. Determine X.

A
150.00
B
165.00
C
177.30
D
190.00
E
200.00

Variant answer in brief

The four-year perpetuity-due factor gives X = 177.30, choice C.

Setup

Convert the annual rate to the effective rate over each four-year payment interval.

j=(1.05)^4-1=0.21550625

Model

Immediate payment timing makes the stream a perpetuity-due on that interval scale.

1000=X\frac{1+j}{j}

Compute

Multiplying value by j divided by one plus j gives 177.2975.

X=1000\frac{j}{1+j}=177.2975

Answer

Each quadrennial grant is 177.30, which is choice C.

\boxed{X=177.30\quad\text{(C)}}

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Cite this solution

ActuaryProof. “SOA Exam FM Sample Question #173 — 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: quadrennial heritage grants

Variant answer in brief

Setup

Model

Compute

Answer

Related Exam FM solutions

Turn this solution into a complete study sequence

Cite this solution