Verified solution · Exam FM

SOA Exam FM Sample Question #135 Solution

This Exam FM sample reference tests Bond Valuation. Evaluating the earliest relevant date in each redemption regime and maturity gives prices 1,308.46, 1,297.58, and 1,309.08; the minimum occurs after coupon 40, so choice C.

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 Valuation question

Setup

Use a half-year yield of 2.5% and identify the price-limiting date in each call-price regime.

P_{20}=35a_{\overline{20}|\,0.025}+1250v^{20}=1308.46

Model

Because each modified coupon rate exceeds the required yield, price within a fixed redemption regime is lowest at that regime's earliest call date.

P_{40}=35a_{\overline{40}|\,0.025}+1125v^{40}=1297.58

Compute

The three necessary endpoint prices are 1,308.46, 1,297.58, and 1,309.08; the middle regime is the smallest.

P_{60}=35a_{\overline{60}|\,0.025}+1000v^{60}=1309.08

Answer

The guaranteed-yield price is therefore controlled by a call immediately after coupon 40, choice C.

\boxed{n=40\quad\text{(C)}}

Calculator reproduction

BA II Plus keystrokes

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

2nd CLR TVM; 2nd I/Y; 1 ENTER; ↓; 1 ENTER; 2nd CPT; 2nd PMT; if BGN is displayed, 2nd ENTER; 2nd CPT; 20 N; 2.5 I/Y; 35 PMT; 1250 FV; CPT PVPV = -1308.46END mode; I/Y is the half-year effective yield for the first redemption regime.
2nd CLR TVM; 2nd I/Y; 1 ENTER; ↓; 1 ENTER; 2nd CPT; 2nd PMT; if BGN is displayed, 2nd ENTER; 2nd CPT; 40 N; 2.5 I/Y; 35 PMT; 1125 FV; CPT PVPV = -1297.58END mode; I/Y is the half-year effective yield for the second redemption regime.
2nd CLR TVM; 2nd I/Y; 1 ENTER; ↓; 1 ENTER; 2nd CPT; 2nd PMT; if BGN is displayed, 2nd ENTER; 2nd CPT; 60 N; 2.5 I/Y; 35 PMT; 1000 FV; CPT PVPV = -1309.09END mode; I/Y is the half-year effective yield through maturity; compare price magnitudes.

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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 is inconsistent with the endpoint prices for all three redemption regimes; no distinct standard single-step error producing it is identifiable.
BChoice B is inconsistent with the endpoint prices for all three redemption regimes; no distinct standard single-step error producing it is identifiable.
DChoice D is inconsistent with the endpoint prices for all three redemption regimes; no distinct standard single-step error producing it is identifiable.
EChoice E is inconsistent with the endpoint prices for all three redemption regimes; no distinct standard single-step error producing it is identifiable.

Original practice · fully worked

Original variant: identifying the limiting call date for a transit note

A transit note pays 60 annually. It may be redeemed for 1,050 after year 5, for 1,020 after year 10, or for 1,000 at maturity in year 15. At a required 5% annual yield, which date produces the lowest acceptable purchase price?

A
Year 5
B
Year 10
C
Year 15
D
Years 5 and 10 tie
E
All dates tie

Variant answer in brief

The endpoint prices are 1,082.47, 1,089.50, and 1,103.80; year 5 is smallest, choice A.

Setup

Each possible redemption creates a different complete cash-flow stream from purchase through that date.

P_5=60a_{\overline5|\,0.05}+1050v^5=1082.47

Model

Price each stream at 5%, including all coupons up to the relevant redemption.

P_{10}=60a_{\overline{10}|\,0.05}+1020v^{10}=1089.50

Compute

The three values increase from 1,082.47 to 1,089.50 to 1,103.80.

P_{15}=60a_{\overline{15}|\,0.05}+1000v^{15}=1103.80

Answer

The earliest redemption limits the guaranteed price, so year 5 and choice A are correct.

\boxed{\min P_t=P_5\quad\text{(A)}}

Calculator reproduction

BA II Plus keystrokes

2nd CLR TVM; 2nd I/Y; 1 ENTER; ↓; 1 ENTER; 2nd CPT; 2nd PMT; if BGN is displayed, 2nd ENTER; 2nd CPT; 5 N; 5 I/Y; 60 PMT; 1050 FV; CPT PVPV = -1082.47END mode; I/Y is the annual required yield for the year-5 call.
2nd CLR TVM; 2nd I/Y; 1 ENTER; ↓; 1 ENTER; 2nd CPT; 2nd PMT; if BGN is displayed, 2nd ENTER; 2nd CPT; 10 N; 5 I/Y; 60 PMT; 1020 FV; CPT PVPV = -1089.50END mode; I/Y is the annual required yield for the year-10 call.
2nd CLR TVM; 2nd I/Y; 1 ENTER; ↓; 1 ENTER; 2nd CPT; 2nd PMT; if BGN is displayed, 2nd ENTER; 2nd CPT; 15 N; 5 I/Y; 60 PMT; 1000 FV; CPT PVPV = -1103.80END mode; I/Y is the annual required yield through maturity; compare price magnitudes.

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Cite this solution

ActuaryProof. “SOA Exam FM Sample Question #135 — Verified Solution.” Verified 2026-07-31.

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

How to solve this Bond Valuation 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: identifying the limiting call date for a transit note

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