Verified solution · Exam FM

SOA Exam FM Sample Question #54 Solution

This Exam FM sample reference tests Dedication Cash-Flow Matching. The backward substitutions give Nᶜ = 0.9524, Nᵇ = 0.9724, and Nᵃ = 0.8807. The requested holding is 0.8807. The result agrees with the published answer key, 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 Dedication Cash-Flow Matching question

Setup

Match liabilities backward from the last date. Security C is the only instrument that can supply the final 100 liability, so determine its holding first.

105N_C=100\Longrightarrow N_C=0.9524

Model

Use the resulting C cash flow in the time-2 equation to obtain the holding of B, then use both earlier cash flows in the time-1 equation for A.

100N_B+5N_C=102\Longrightarrow N_B=0.9724

Compute

The backward substitutions give Nᶜ = 0.9524, Nᵇ = 0.9724, and Nᵃ = 0.8807. The requested holding is 0.8807.

107N_A+5N_C=99\Longrightarrow N_A=0.8807

Answer

The calculation gives 0.8807 for dedication cash-flow matching, matching published choice A.

\boxed{N_A=0.8807\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 (0.8901) does not match the checked dedication cash-flow matching result (0.8807); no distinct standard one-step error is identifiable.
CChoice C (0.8975) does not match the checked dedication cash-flow matching result (0.8807); no distinct standard one-step error is identifiable.
DChoice D (0.9524) does not match the checked dedication cash-flow matching result (0.8807); no distinct standard one-step error is identifiable.
EChoice E (0.9724) does not match the checked dedication cash-flow matching result (0.8807); no distinct standard one-step error is identifiable.

Original practice · fully worked

Original variant: backward dedication with two bespoke notes

A foundation must pay 400 at the end of year 1 and 800 at the end of year 3. Note A pays 420 at year 1 only. Note B pays 50 at year 1 and 850 at year 3. Find the number of units of Note A in an exact cash-flow dedication.

A
0.7626
B
0.8041
C
0.8403
D
0.8952
E
0.9524

Variant answer in brief

The Note B holding is 0.941176 and the remaining year-1 need requires 0.840336 units of Note A. The required Note A holding is 0.8403, which is choice C.

Setup

Let a and b be note holdings and match each liability date without introducing an interest-rate assumption.

420a+50b=400,\qquad850b=800

Model

Solve the year-3 equation first because only Note B pays at that date, then substitute its holding into the year-1 equation.

b=800/850=0.941176

Compute

The Note B holding is 0.941176 and the remaining year-1 need requires 0.840336 units of Note A.

a=\frac{400-50(0.941176)}{420}=0.840336

Answer

The required Note A holding is 0.8403, which is choice C.

\boxed{a=0.8403\quad\text{(C)}}

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Cite this solution

ActuaryProof. “SOA Exam FM Sample Question #54 — Verified Solution.” Verified 2026-07-31.

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

How to solve this Dedication Cash-Flow Matching question

Setup

Model

Compute

Answer

All 461 Exam FM sample solutions in syllabus order

Why the other letters tempt

Original variant: backward dedication with two bespoke notes

Variant answer in brief

Setup

Model

Compute

Answer

Related Exam FM solutions

Turn this solution into a complete study sequence

Cite this solution