Verified solution · Exam FM

SOA Exam FM Sample Question #39 Solution

This Exam FM sample reference tests Forward-Rate Cash-Flow Matching. Adding the two costs gives 2,583.66, which rounds to 2,584. 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 Forward-Rate Cash-Flow Matching question

Setup

Price each dedicated asset separately. The first 1,000 liability is funded by a one-year zero at 6%; the second is funded using the quoted one-year forward rate and its spot discounting path.

P_1=1000/1.06=943.40

Model

The first present value is 943.40. Converting the second liability through its forward contract gives a time-2 requirement of 1,877.93 and a time-0 cost of 1,640.26.

F_2=2000/1.065=1877.93,\quad P_2=F_2/1.07^2=1640.26

Compute

Adding the two costs gives 2,583.66, which rounds to 2,584.

P=P_1+P_2=2583.66

Answer

The calculation gives 2584 for forward-rate cash-flow matching, matching published choice A.

\boxed{P=2584\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 (2697) does not match the checked forward-rate cash-flow matching result (2584); no distinct standard one-step error is identifiable.
CChoice C (2801) does not match the checked forward-rate cash-flow matching result (2584); no distinct standard one-step error is identifiable.
DChoice D (2907) does not match the checked forward-rate cash-flow matching result (2584); no distinct standard one-step error is identifiable.
EChoice E (3000) does not match the checked forward-rate cash-flow matching result (2584); no distinct standard one-step error is identifiable.

Original practice · fully worked

Original variant: zero-coupon match with reinvestment

Liabilities of 1,000 and 1,500 are due in years 1 and 3. One-year zeros yield 5%, two-year zeros yield 6%, and proceeds at year 2 reinvest one year at 4%. Find today's total cost.

A
2100.0
B
2200.0
C
2236.0
D
2300.0
E
2400.0

Variant answer in brief

The two purchase costs sum to 2,236.0297, or 2,236.0. This selects choice C.

Setup

Price the first liability directly at the one-year spot rate.

P_1=1000/1.05

Model

For the second, divide by the one-year forward accumulation and then by the two-year spot accumulation.

P_2=(1500/1.04)/1.06^2

Compute

The two purchase costs sum to 2,236.0297, or 2,236.0.

P_1+P_2=2236.0297

Answer

The requested value is 2236.0, so the correct choice is C.

\boxed{P=2236.0\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 #39 — Verified Solution.” Verified 2026-07-31.

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

How to solve this Forward-Rate Cash-Flow Matching question

Setup

Model

Compute

Answer

All 461 Exam FM sample solutions in syllabus order

Why the other letters tempt

Original variant: zero-coupon match with reinvestment

Variant answer in brief

Setup

Model

Compute

Answer

Related Exam FM solutions

Turn this solution into a complete study sequence

Cite this solution