Verified solution · Exam FM

SOA Exam FM Sample Question #44 Solution

This Exam FM sample reference tests Duration Immunization. The liability value is 335,530.30 and its duration is 6.89214. Solving the duration equation gives X = 208,556, which rounds to 208,600. The result agrees with the published answer key, choice C.

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 Duration Immunization question

Setup

First value the fifteen-payment liability at 6.2% and compute its Macaulay duration from the discounted time-weighted cash flows.

PV_L=35000a_{\overline{15}|\,0.062}=335530.30

Model

Let X be the present-value amount in the five-year zero; the remainder of the liability present value goes into the ten-year zero. Equal duration gives a linear weighted-time equation.

D_L=\frac{\sum_{t=1}^{15}t(35000)v^t}{PV_L}=6.89214

Compute

The liability value is 335,530.30 and its duration is 6.89214. Solving the duration equation gives X = 208,556, which rounds to 208,600.

5X+10(PV_L-X)=D_LPV_L\Longrightarrow X=208556

Answer

The calculation gives 208,600 for duration immunization, matching published choice C.

\boxed{X=208600\quad\text{(C)}}

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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 (127,000) does not match the checked duration immunization result (208,600); no distinct standard one-step error is identifiable.
BChoice B (167,800) does not match the checked duration immunization result (208,600); no distinct standard one-step error is identifiable.
DChoice D (247,900) does not match the checked duration immunization result (208,600); no distinct standard one-step error is identifiable.
EChoice E (292,800) does not match the checked duration immunization result (208,600); no distinct standard one-step error is identifiable.

Original practice · fully worked

Original variant: two-zero immunization mix

A liability pays 10,000 annually for ten years. At 5%, immunize it using three-year and eight-year zero-coupon bonds. Find the amount invested in the three-year zeros.

A
40000
B
43000
C
44800
D
47000
E
50000

Variant answer in brief

The three-year allocation is 44,800.19, or 44,800. This selects choice C.

Setup

Value the ten-payment liability and calculate its discounted time-weighted average.

PV_L=10000a_{\overline{10}|\,0.05},\quad D_L=\frac{\sum t(10000)v^t}{PV_L}

Model

Allocate liability present value between three-year and eight-year zeros so their weighted duration matches the liability.

3X+8(PV_L-X)=D_LPV_L

Compute

The three-year allocation is 44,800.19, or 44,800.

X=44800.19

Answer

The requested value is 44800, so the correct choice is C.

\boxed{X=44800\quad\text{(C)}}

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Cite this solution

ActuaryProof. “SOA Exam FM Sample Question #44 — Verified Solution.” Verified 2026-07-31.

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

How to solve this Duration Immunization question

Setup

Model

Compute

Answer

All 461 Exam FM sample solutions in syllabus order

Why the other letters tempt

Original variant: two-zero immunization mix

Variant answer in brief

Setup

Model

Compute

Answer

Related Exam FM solutions

Turn this solution into a complete study sequence

Cite this solution