Verified solution · Exam FM

SOA Exam FM Sample Question #431 Solution

This Exam FM sample reference tests Bond Premium Amortization. The semiannual yield is 2.469508%. Prospective book values after coupons 11 and 12 are 1042.35 and 1038.09, so the twelfth premium amortization is 4.26, 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 Bond Premium Amortization question

Setup

Convert the 5% annual effective yield to the semiannual coupon-period yield.

j=(1.05)^{1/2}-1=0.0246950766

C=30

Model

Immediately after coupon k, value the remaining coupons and redemption prospectively.

B_k=30a_{\overline{20-k}|j}+1{,}000(1+j)^{-(20-k)}

Compute

Evaluate consecutive book values around the twelfth coupon. Their decline is the premium amortized in that coupon.

B_{11}=1{,}042.3457

B_{12}=1{,}038.0865

B_{11}-B_{12}=4.2592

Answer

The premium amortization is 4.26, choice E.

\boxed{4.26\quad\text{(E)}}

Calculator reproduction

BA II Plus keystrokes

Check END/BGN, period, sign, TVM, and cash-flow setup

8 · N; 2.4695077 · I/Y; 30 · PMT; 1000 · FV; CPT · PV−1038.0865Eight coupons remain immediately after coupon 12.

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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 uses a 2.5% half-year approximation and rounds intermediate book values before taking their difference.
BChoice B computes interest on redemption value rather than on the book value before the twelfth coupon.
CChoice C treats the premium as amortizing by a constant amount over all coupon periods.
DChoice D uses the book value after coupon 12 as the interest base; effective-interest amortization uses the preceding book value.

Original practice · fully worked

Original variant: recover a coupon from book values

A premium bond has book value 1,080 immediately after its fifth annual coupon and 1,070 immediately after its sixth annual coupon. Its annual effective yield is 3%. Determine the annual coupon amount.

A
30.00
B
32.40
C
40.00
D
42.40
E
52.40

Variant answer in brief

The book-value recursion is B6 = 1.03 B5 minus C. Solving gives a coupon of 42.40, choice D.

Setup

Use the effective-interest book-value recursion between consecutive post-coupon dates.

B_6=B_5(1+i)-C

Model

Insert the two book values and the annual yield.

1{,}070=1{,}080(1.03)-C

Compute

Solve for the coupon paid at the end of the period.

C=1{,}080(1.03)-1{,}070=42.40

Answer

The annual coupon is 42.40, choice D.

\boxed{C=42.40\quad\text{(D)}}

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Cite this solution

ActuaryProof. “SOA Exam FM Sample Question #431 — Verified Solution.” Verified 2026-07-31.

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

How to solve this Bond Premium Amortization question

Setup

Model

Compute

Answer

BA II Plus keystrokes

All 461 Exam FM sample solutions in syllabus order

Why the other letters tempt

Original variant: recover a coupon from book values

Variant answer in brief

Setup

Model

Compute

Answer

Related Exam FM solutions

Turn this solution into a complete study sequence

Cite this solution