Verified solution · Exam FM

SOA Exam FM Sample Question #292 Solution

This Exam FM sample reference tests Bond Pricing and Yields. Because the bond is bought at a premium, the earliest permissible call is adverse to the investor. Converting 7% annual effective to half-year yield 3.4408% and pricing 30 periods to the year-15 call gives 1103.61, choice B.

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 Pricing and Yields question

Setup

The coupon rate exceeds yield, so use the earliest call date at year 15 when pricing to the investor's minimum yield.

n=30\text{ half-year periods}

Model

Convert the annual effective yield to an equivalent half-year rate.

j=(1.07)^{1/2}-1

Compute

Discount 30 coupons of 40 and the 1,000 call payment at j, giving 1103.614560.

P=40a_{\overline{30}|j}+1000(1+j)^{-30}

P=1103.61456002

Answer

The purchase price is approximately 1,104, selecting choice B.

\boxed{P\approx1104\quad\text{(B)}}

Calculator reproduction

BA II Plus keystrokes

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

2ND · CLR TVM · 30 · N · 3.440804 · I/Y · 40 · PMT · 1000 · FV · CPT · PVPV = -1103.61

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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 (1067) does not satisfy the earliest-call cash-flow price at the half-year rate equivalent to 7% annually; no distinct standard one-step error is identifiable.
CChoice C (1132) does not satisfy the earliest-call cash-flow price at the half-year rate equivalent to 7% annually; no distinct standard one-step error is identifiable.
DChoice D (1141) does not satisfy the earliest-call cash-flow price at the half-year rate equivalent to 7% annually; no distinct standard one-step error is identifiable.
EChoice E (1154) does not satisfy the earliest-call cash-flow price at the half-year rate equivalent to 7% annually; no distinct standard one-step error is identifiable.

Original practice · fully worked

Original variant: maximum price consistent with a guaranteed callable-bond yield

A bond pays 40 semiannually and may be called for 1,000 after year 5 or mature for 1,000 after year 10. What is the maximum purchase price that guarantees at least 6% nominal annual yield convertible semiannually?

A
1,085.30
B
1,139.57
C
1,193.83
D
1,248.10
E
1,302.36

Variant answer in brief

At the target 3% half-year yield, the coupon exceeds the yield-rate payment, so the earliest call produces the lowest acceptable price. Pricing ten coupons and redemption gives 1,085.30, choice A.

Setup

Convert the guaranteed nominal yield to 3% per half-year.

j=0.06/2=0.03

Model

Because the coupon stream is premium-producing at 3%, the five-year call is the adverse redemption scenario.

P_{\max}=40a_{\overline{10}|0.03}+1000(1.03)^{-10}

Compute

The controlling scenario price is 1085.30.

P_{\max}=1085.30202837

Answer

The maximum qualifying purchase price is 1,085.30, selecting choice A.

\boxed{P_{\max}\approx1085.30\quad\text{(A)}}

Calculator reproduction

BA II Plus keystrokes

2ND · CLR TVM · 10 · N · 3 · I/Y · 40 · PMT · 1000 · FV · CPT · PVPV = -1085.30

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Cite this solution

ActuaryProof. “SOA Exam FM Sample Question #292 — Verified Solution.” Verified 2026-07-31.

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

How to solve this Bond Pricing and Yields 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: maximum price consistent with a guaranteed callable-bond yield

Variant answer in brief

Setup

Model

Compute

Answer

BA II Plus keystrokes

Related Exam FM solutions

Turn this solution into a complete study sequence

Cite this solution