Verified solution · Exam FM

SOA Exam FM Sample Question #372 Solution

This Exam FM sample reference tests Duration and Convexity. Discounted coupons and redemption have total price 1,216.47 and time-weighted value 5,173.27; their ratio is 4.2535 years, nearest choice E.

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

Place the five coupons at years one through five and redemption at year five.

P=100a_{\overline{5}|\,0.05}+1000v^5=1216.47

Model

Macaulay duration uses each discounted cash flow multiplied by its payment year.

M=100\sum_{t=1}^{5}tv^t+5(1000)v^5

Compute

Dividing the time-weighted present value by the verified bond price gives 4.2535 years.

D_M=\frac{M}{P}=4.2535

Answer

The closest listed duration is 4.3 years, corresponding to choice E.

\boxed{D_M\approx4.3\text{ years}\quad\text{(E)}}

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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 coupon-and-redemption present-value duration ratio; no distinct standard single-step error producing it is identifiable.
BChoice B is inconsistent with the coupon-and-redemption present-value duration ratio; no distinct standard single-step error producing it is identifiable.
CChoice C is inconsistent with the coupon-and-redemption present-value duration ratio; no distinct standard single-step error producing it is identifiable.
DChoice D is inconsistent with the coupon-and-redemption present-value duration ratio; no distinct standard single-step error producing it is identifiable.

Original practice · fully worked

Original variant: redemption amount implied by a target duration

A five-year bond pays 80 annually and yields 6% effective. Its Macaulay duration is 4.20 years. Determine its redemption payment at year 5.

A
622.05
B
682.05
C
742.05
D
802.05
E
862.05

Variant answer in brief

Solving the duration equation for the year-five redemption gives 742.05, choice C.

Setup

Treat the unknown redemption as an additional year-five cash flow beyond the coupons.

4.20=\frac{80\sum_{t=1}^{5}tv^t+5Rv^5}{80a_{\overline{5}|\,0.06}+Rv^5}

Model

Cross-multiply the target-duration ratio so the equation is linear in redemption.

(5-4.20)Rv^5=4.20(80a_{\overline{5}|})-80\sum_{t=1}^{5}tv^t

Compute

Using the 6% discount factor yields redemption 742.0481.

R=742.0481

Answer

The required year-five redemption is 742.05, corresponding to choice C.

\boxed{R=742.05\quad\text{(C)}}

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Cite this solution

ActuaryProof. “SOA Exam FM Sample Question #372 — 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: redemption amount implied by 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