Worked solution · Exam FM

SOA Exam FM Sample Question #308 Solution

This Exam FM sample reference tests Immunization and Asset-Liability Management. Backward cash matching gives faces 1,000 for Bond III, 980.39 for Bond II, and 970.69 for Bond I. Pricing each bond at its own yield gives total 2241.82, so choice D is correct.

Independent analysis by ActuaryProof · reviewed October 6, 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 Immunization and Asset-Liability Management question

Setup

Match the year-3 liability with the zero-coupon face, then match year 2 with Bond II coupon plus redemption.

F_3=1000

1.02F_2=1000

Model

At year 1, Bond I maturity plus Bond II's first coupon must total 1,000.

1.01F_1+0.02F_2=1000

Compute

The faces are F1 = 970.6853, F2 = 980.3922, and F3 = 1,000. Discounting their cash flows at 14%, 15%, and 18% gives 2241.817958.

P=2241.81795841

Answer

The total purchase price is approximately 2,242, selecting choice D.

\boxed{P\approx2242\quad\text{(D)}}

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Financial Mathematics Duration & Immunization Workbook

30 original general cash flows, portfolios, and asset liability management problems with complete solutions and wrong-choice analysis. Written for Exam FM, not copied from the SOA set. One-time $19 PDF.

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Original practice · fully worked

Original variant: first-year cash-flow shortfall diagnosed from a bond portfolio

A portfolio holds a one-year bond with face 800 and coupon rate 1%, plus a two-year bond with face 1,000 and annual coupon rate 2%. A liability of 1,000 is due at year 1. Ignoring any year-3 asset, calculate the year-1 cash-flow shortfall.

A
163.40
B
172.00
C
180.60
D
189.20
E
197.80

Answer and calculation

The one-year bond supplies 808 and the two-year bond supplies its first coupon of 20. Total year-1 assets are 828, leaving shortfall 172, choice B.

Setup

Compute the one-year bond's coupon-plus-redemption maturity cash flow.

C_1=800(1.01)=808

Model

Add the first coupon from the still-outstanding two-year bond.

A_1=808+0.02(1000)=828

Compute

Subtract available year-1 assets from the liability.

S_1=1000-828=172

Answer

The year-1 shortfall is 172, selecting choice B.

\boxed{S_1=172\quad\text{(B)}}

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How to solve this Immunization and Asset-Liability Management question

Setup

Model

Compute

Answer

Financial Mathematics Duration & Immunization Workbook

Original variant: first-year cash-flow shortfall diagnosed from a bond portfolio

Answer and calculation

Setup

Model

Compute

Answer

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Next steps for Exam FM General Cash Flows, Portfolios, and Asset Liability Management