Worked solution · Exam FM

SOA Exam FM Sample Question #148 Solution

This Exam FM sample reference tests Cash-Flow and Risk Matching. The exact-match combinations are two units of J for 3,000, one K plus two L for 2,500, or one M for 4,000; the minimum is 2,500, choice C.

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.

Read the solution Open official source

Independent solution

How to solve this Cash-Flow and Risk Matching question

Setup

Full cash-flow matching requires 1,000 at each of the five year-ends and permits only whole investment units.

2J:\quad C=2(1500)=3000

Model

Enumerate the combinations whose dated cash flows exactly reproduce that five-entry liability vector.

K+2L:\quad C=500+2(1000)=2500

Compute

The feasible costs are 3,000, 2,500, and 4,000; K supplies year five while two L units supply years one through four.

M:\quad C=4000

Answer

The least exact-match cost is 2,500, corresponding to choice C.

\boxed{C_{\min}=2500\quad\text{(C)}}

Test the method on unseen problems

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.

See the cover and sample pages

Original practice · fully worked

Original variant: whole-unit funding for a three-year festival

A festival owes 500 at each of years 1, 2, and 3. Investment A costs 850 and pays 500 in years 1 and 2. Investment B costs 350 and pays 500 in year 3. Investment C costs 1,300 and pays 500 in all three years. Whole units only are allowed. Find the least cost of an exact match.

A
850
B
1,000
C
1,200
D
1,300
E
1,550

Answer and calculation

One A plus one B exactly covers all three dates for 1,200, less than one C; choice C.

Setup

Translate each whole-unit investment into a three-entry dated cash-flow vector.

CF_A=(500,500,0),\quad CF_B=(0,0,500)

Model

Adding one A and one B reproduces the liability vector exactly.

CF_A+CF_B=(500,500,500)

Compute

That pair costs 1,200, while the only other one-unit exact match, C, costs 1,300.

C_{A+B}=850+350=1200<1300=C_C

Answer

The least exact-match cost is 1,200, choice C.

\boxed{C_{\min}=1200\quad\text{(C)}}

Keep practicing

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

Work through the related free solutions for this topic, review the formulas you used, or keep every current Exam FM solution in one searchable PDF.

More Exam FM General Cash Flows, Portfolios, and Asset Liability Management practice problems Free Exam FM formula sheet Exam FM study manual PDF — $49

How to solve this Cash-Flow and Risk Matching question

Setup

Model

Compute

Answer

Financial Mathematics Duration & Immunization Workbook

Original variant: whole-unit funding for a three-year festival

Answer and calculation

Setup

Model

Compute

Answer

Related Exam FM solutions

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