Verified solution · Exam FM

SOA Exam FM Sample Question #301 Solution

This Exam FM sample reference tests Bond Pricing and Yields. The half-year coupon rate 4% exceeds the half-year yield equivalent to 6% annually, so the earliest year-5 call is worst for the investor. Pricing ten coupons and par at that rate gives 108.92, so choice A is correct.

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.

Read the solution Open official source

Independent solution

How to solve this Bond Pricing and Yields question

Setup

Convert the 6% annual effective target to its equivalent half-year yield.

j=(1.06)^{1/2}-1

Model

Because the coupon is above yield, use the earliest allowable call at year 5, or ten half-year periods.

P_{\max}=4a_{\overline{10}|j}+100(1+j)^{-10}

Compute

The controlling call-scenario price is 108.922848.

P_{\max}=108.92284825

Answer

The maximum price is approximately 108.92, selecting choice A.

\boxed{P_{\max}\approx108.92\quad\text{(A)}}

Calculator reproduction

BA II Plus keystrokes

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

2ND · CLR TVM · 10 · N · 2.956301 · I/Y · 4 · PMT · 100 · FV · CPT · PVPV = -108.92

Continue without hunting through PDFs

All 461 Exam FM sample solutions in syllabus order

The searchable 2210-page manual includes this complete solution, its error analysis, and one original worked variant for every active reference.

See inside the Exam FM study manual PDF

Error diagnosis

Why the other letters tempt

These notes identify the calculation error associated with each wrong letter when that error is reproducible.

BChoice B (111.83) does not satisfy the minimum scenario price among the callable dates at the target annual yield; no distinct standard one-step error is identifiable.
CChoice C (114.41) does not satisfy the minimum scenario price among the callable dates at the target annual yield; no distinct standard one-step error is identifiable.
DChoice D (115.59) does not satisfy the minimum scenario price among the callable dates at the target annual yield; no distinct standard one-step error is identifiable.
EChoice E (116.74) does not satisfy the minimum scenario price among the callable dates at the target annual yield; no distinct standard one-step error is identifiable.

Original practice · fully worked

Original variant: yield to worst from several possible redemption dates

A bond costs 108, pays 4 every half-year, and redeems 100. It may be called after years 3 or 6, or mature after year 10. Calculate the annual effective yield to worst.

A
4.38%
B
4.64%
C
4.90%
D
5.16%
E
5.41%

Variant answer in brief

Solving the three possible redemption yields and converting the smallest half-year root to annual effective gives yield to worst 5.16%, choice D.

Setup

Solve a half-year yield for each possible redemption period using the common price, coupon, and redemption.

108=4a_{\overline n|j_n}+100(1+j_n)^{-n}

n\in\{6,12,20\}

Model

The guaranteed return is the smallest scenario yield, converted to annual effective form.

j_{\min}=\min(j_6,j_{12},j_{20})

i_{\mathrm{worst}}=(1+j_{\min})^2-1

Compute

The scenario half-year yields are 2.5454%, 3.1873%, 3.4402%; the annualized minimum is 5.1556%.

i_{\mathrm{worst}}=0.0515557927

Answer

The annual effective yield to worst is 5.16%, selecting choice D.

\boxed{i_{\mathrm{worst}}\approx5.16\%\quad\text{(D)}}

Calculator reproduction

BA II Plus keystrokes

2ND · CLR TVM · 6 · N · 108 · +/- · PV · 4 · PMT · 100 · FV · CPT · I/YI/Y = 2.5454
12 · N · CPT · I/YI/Y = 3.1873
20 · N · CPT · I/YI/Y = 3.4402

Keep practicing

Turn this solution into a complete study sequence

The 2210-page Financial Mathematics Proof Manual reorganizes 461 verified Exam FM solutions by syllabus skill and adds formula proofs, error patterns, and original worked practice.

See the Exam FM study manual PDF — $49 More Exam FM Bonds practice problems Free Exam FM formula sheet

Cite this solution

ActuaryProof. “SOA Exam FM Sample Question #301 — 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: yield to worst from several possible redemption dates

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