Verified solution · Exam FM

SOA Exam FM Sample Question #429 Solution

This Exam FM sample reference tests Bond Modified Duration. Present-value weighting gives Macaulay duration 6.89216 years. Dividing by 1.10 gives modified duration 6.26560, which rounds to 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 Bond Modified Duration question

Setup

Scale face amount to 1000 without changing duration. Annual cash flows are 90 for years 1 through 9 and 1090 at year 10.

v=(1.10)^{-1}

Model

Compute price and the time-weighted present-value numerator.

P=90a_{\overline{10}|0.10}+1{,}000v^{10}

N=\sum_{t=1}^{9}t(90)v^t+10(1{,}090)v^{10}

Compute

The price is 938.5543 and Macaulay duration is 6.892158. Convert to modified duration.

D_{\mathrm{Mac}}=\frac{N}{P}=6.892158

D_{\mathrm{mod}}=\frac{D_{\mathrm{Mac}}}{1.10}=6.265598

Answer

The modified duration is 6.27 years, choice A.

\boxed{D_{\mathrm{mod}}\approx6.27\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 is a nearby rounding value but does not equal the time-weighted present value divided by price and then by 1.10.
CChoice C can result from omitting part of the redemption from the duration numerator, changing the late-cash-flow weight.
DChoice D reports the Macaulay duration 6.89216 before conversion to modified duration.
EChoice E gives excessive weight to the tenth-year redemption by excluding coupons from the price denominator.

Original practice · fully worked

Original variant: duration estimate of a yield shock

A seven-year corporate bond has Macaulay duration 7.2 years at an annual effective yield of 8%. Estimate the percentage price change, using modified duration, if the yield rises by 20 basis points.

A
−1.56%
B
−1.44%
C
−1.33%
D
+1.33%
E
+1.56%

Variant answer in brief

Modified duration is 7.2 divided by 1.08. Multiplying its negative by the 0.002 yield increase gives an estimated price change of negative 1.333%, choice C.

Setup

Convert the given Macaulay duration to modified duration at the current yield.

D_{\mathrm{mod}}=\frac{7.2}{1.08}=6.666667

Model

The first-order relative price change is negative modified duration times the yield change.

\frac{\Delta P}{P}\approx-D_{\mathrm{mod}}\Delta i

Compute

Insert a positive 20-basis-point change.

\frac{\Delta P}{P}\approx-6.666667(0.002)=-0.013333

Answer

The estimated decline is 1.33%, choice C.

\boxed{\Delta P/P\approx-1.33\%\quad\text{(C)}}

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ActuaryProof. “SOA Exam FM Sample Question #429 — Verified Solution.” Verified 2026-07-31.

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

How to solve this Bond Modified Duration question

Setup

Model

Compute

Answer

All 461 Exam FM sample solutions in syllabus order

Why the other letters tempt

Original variant: duration estimate of a yield shock

Variant answer in brief

Setup

Model

Compute

Answer

Related Exam FM solutions

Turn this solution into a complete study sequence

Cite this solution