Verified solution · Exam FM

SOA Exam FM Sample Question #383 Solution

This Exam FM sample reference tests Duration and Convexity. The stated liability duration determines the five-year discount factor and yield; dividing 3.70 by one plus that yield gives modified duration 3.3057 years, choice B.

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 and Convexity question

Setup

The immediate liability contributes value but zero to the duration numerator.

3.70=\frac{5(100000)v^5}{20000+100000v^5}

Model

Use the stated weighted time to solve for the five-year discount factor and hence the annual yield factor.

v^5=\frac{3.70}{6.50},\qquad 1+i=1.11929

Compute

Convert Macaulay duration to modified duration by dividing by one plus yield.

D_{\mathrm{mod}}=\frac{3.70}{1.11929}=3.30567

Answer

The modified duration is approximately 3.31 years, corresponding to choice B.

\boxed{D_{\mathrm{mod}}\approx3.31\quad\text{(B)}}

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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 is inconsistent with the two-liability duration equation and modified-duration conversion; no distinct standard single-step error producing it is identifiable.
CChoice C is inconsistent with the two-liability duration equation and modified-duration conversion; no distinct standard single-step error producing it is identifiable.
DChoice D is inconsistent with the two-liability duration equation and modified-duration conversion; no distinct standard single-step error producing it is identifiable.
EChoice E is inconsistent with the two-liability duration equation and modified-duration conversion; no distinct standard single-step error producing it is identifiable.

Original practice · fully worked

Original variant: future liability amount from a target duration

A company owes 20,000 today and F in five years. At 5% effective annually, the combined Macaulay duration is 3.00 years. Determine F.

A
32,288.45
B
35,288.45
C
38,288.45
D
41,288.45
E
44,288.45

Variant answer in brief

Target duration 3 requires the discounted future liability to equal 30,000, so F = 38,288.45, choice C.

Setup

The time-zero obligation enters the denominator but not the time-weighted numerator.

3=\frac{5Fv^5}{20000+Fv^5}

Model

Cross-multiply the target-duration equation to isolate the discounted future amount.

60000+3Fv^5=5Fv^5

Compute

Its present value must be 30,000, which accumulates to 38,288.4469 in year five.

Fv^5=30000,\qquad F=30000(1.05)^5=38288.4469

Answer

The future liability is 38,288.45, corresponding to choice C.

\boxed{F=38288.45\quad\text{(C)}}

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Cite this solution

ActuaryProof. “SOA Exam FM Sample Question #383 — Verified Solution.” Verified 2026-07-31.

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

How to solve this Duration and Convexity question

Setup

Model

Compute

Answer

All 461 Exam FM sample solutions in syllabus order

Why the other letters tempt

Original variant: future liability amount from 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