Verified solution · Exam FM

SOA Exam FM Sample Question #447 Solution

This Exam FM sample reference tests Perpetuity Duration Conversion. The immediate-perpetuity Macaulay duration 32.25 implies i = 3.2%. A due perpetuity then has Macaulay duration 31.25 and modified duration 30.2810, 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 Perpetuity Duration Conversion question

Setup

Payment scale does not affect duration. Use the level perpetuity-immediate duration to recover the yield.

D_{\mathrm{Mac,imm}}=\frac{1+i}{i}=32.25

Model

Solve for i, then write the due-perpetuity Macaulay duration.

i=\frac{1}{31.25}=0.032

D_{\mathrm{Mac,due}}=\frac1i=31.25

Compute

Convert the due duration to modified duration.

D_{\mathrm{mod,due}}=\frac{31.25}{1.032}=30.281008

Answer

The modified duration is 30.28, choice A.

\boxed{X\approx30.28\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 uses an interest rate inferred from 32.25 as though that number were 1 divided by i.
CChoice C reports the due perpetuity's Macaulay duration without dividing by one plus i.
DChoice D converts the immediate perpetuity's duration rather than first shifting to due timing.
EChoice E lets the 1.02 payment multiplier alter duration even though common cash-flow scale cancels.

Original practice · fully worked

Original variant: yield from due-perpetuity modified duration

A level annual perpetuity-due has modified duration 15 years. Determine the annual effective yield.

A
5.00%
B
5.89%
C
6.27%
D
6.67%
E
7.18%

Variant answer in brief

For a perpetuity-due, modified duration is 1 divided by i times 1 plus i. Solving the resulting quadratic gives i = 6.2731%, choice C.

Setup

Use the modified-duration formula obtained from the due-perpetuity price.

15=\frac{1}{i(1+i)}

Model

Rearrange to a quadratic in i.

i^2+i-\frac1{15}=0

Compute

Select the positive root because an effective yield must exceed zero here.

i=\frac{-1+\sqrt{1+4/15}}2=0.0627314

Answer

The annual effective yield is 6.27%, choice C.

\boxed{i\approx6.27\%\quad\text{(C)}}

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ActuaryProof. “SOA Exam FM Sample Question #447 — Verified Solution.” Verified 2026-07-31.

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

How to solve this Perpetuity Duration Conversion question

Setup

Model

Compute

Answer

All 461 Exam FM sample solutions in syllabus order

Why the other letters tempt

Original variant: yield from due-perpetuity modified duration

Variant answer in brief

Setup

Model

Compute

Answer

Related Exam FM solutions

Turn this solution into a complete study sequence

Cite this solution