Verified solution · Exam FM
This Exam FM sample reference tests Immunization and Asset-Liability Management. The 9,465 price of the two-year 5% coupon bond at 8% implies face 10,000. It funds 10,500 at year 2, so the year-1 liability is 5,250; after the 500 coupon, the one-year zero must supply 4,750, costing 4481.13 and choice C.
Independent solution
Setup
Recover the face amount of the two-year bond from its purchase price.
Model
The year-2 maturity equals the second liability, which is twice the year-1 liability.
Compute
Face is 10000, so L1 = 5250. After the year-1 coupon of 500, the remaining amount discounted at 6% costs 4481.13.
Answer
The one-year bond investment is approximately 4,481, selecting choice C.
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Original practice · fully worked
An insurer holds a two-year par bond with face 8,000 and annual coupon rate 4%, plus 5,000 invested in a one-year zero yielding 5%. The assets exactly match liabilities at years 1 and 2. Calculate the year-2 liability divided by the year-1 liability.
The year-1 assets provide 5570.00, and the year-2 bond maturity provides 8320.00. Their ratio is 1.4937, choice B.
Setup
Add the one-year zero maturity and the first bond coupon for the year-1 asset cash flow.
Model
The year-2 asset cash flow is the second coupon plus redemption.
Compute
The matched liabilities are 5570.00 and 8320.00, giving ratio 1.493716.
Answer
The liability ratio is 1.4937, selecting choice B.
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ActuaryProof. “SOA Exam FM Sample Question #274 — Verified Solution.” Verified 2026-07-31.
Source reference: official SOA sample-question PDF. Last reviewed 2026-07-31.
