Verified solution · Exam FM

SOA Exam FM Sample Question #338 Solution

This Exam FM sample reference tests Single-Liability Duration Matching. The assets already have present value 50000. Their Macaulay duration is the value-weighted maturity 30.8 years. The liability present value is also 50000 and its duration is y, so y = 30.80, 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 Single-Liability Duration Matching question

Setup

At 7.5%, the stated liability amount at time y discounts to 50000.

PV_L=\frac{50{,}000(1.075)^y}{(1.075)^y}=50{,}000

Model

The two zero-coupon assets also total 50000 in present value.

PV_A=30{,}000+20{,}000=50{,}000

Compute

A zero's duration equals its maturity, so compute the asset weighted average.

D_A=\frac{30{,}000(28)+20{,}000(35)}{50{,}000}=30.8

D_L=y

Answer

Duration matching requires y = 30.80, choice A.

\boxed{y=30.80\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 discounts the asset present-value weights a second time before averaging maturities.
CChoice C takes the unweighted midpoint of 28 and 35 rather than the 60%-40% value weights.
DChoice D reverses the 30000 and 20000 weights on the two zero maturities.
EChoice E adds a convexity adjustment even though y is fixed by the first-order duration condition.

Original practice · fully worked

Original variant: long-zero share for a target duration

A single liability has Macaulay duration 9 years. It is matched using zero-coupon assets maturing in 4 and 14 years. What fraction of asset present value must be invested in the 14-year zero to match duration?

A
30%
B
40%
C
50%
D
60%
E
70%

Variant answer in brief

A weighted average of maturities 4 and 14 equals 9 only when the long-zero present-value share is 50%, choice C.

Setup

Let w be the present-value fraction in the 14-year zero.

D_A=4(1-w)+14w

Model

Set asset duration equal to the liability duration.

4+10w=9

Compute

Solve the linear weight equation.

w=0.50

Answer

Half of present value belongs in the long zero, choice C.

\boxed{w=50\%\quad\text{(C)}}

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ActuaryProof. “SOA Exam FM Sample Question #338 — Verified Solution.” Verified 2026-07-31.

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

How to solve this Single-Liability Duration Matching question

Setup

Model

Compute

Answer

All 461 Exam FM sample solutions in syllabus order

Why the other letters tempt

Original variant: long-zero share for a target duration

Variant answer in brief

Setup

Model

Compute

Answer

Related Exam FM solutions

Turn this solution into a complete study sequence

Cite this solution