Verified solution · Exam FM

SOA Exam FM Sample Question #239 Solution

This Exam FM sample reference tests Bond Pricing and Yields. Write the four-year price with eight half-year cash flows and the two-year price with four. The shorter price is 93% of the longer price; solving that relation gives redemption 455.37, 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.

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Independent solution

How to solve this Bond Pricing and Yields question

Setup

Use half-year periods with coupon 25 and yield 3% per period.

P_8=25a_{\overline8|0.03}+Cv^8

P_4=25a_{\overline4|0.03}+Cv^4

Model

The hypothetical two-year price is 7% lower than the actual four-year price.

P_4=0.93P_8

Compute

Substituting both price formulas and isolating C gives redemption 455.3712.

C=455.37122813

Answer

The redemption value is approximately 455, selecting choice A.

\boxed{C\approx455\quad\text{(A)}}

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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.

BChoice B (469) does not satisfy the equality P4 = 0.93 P8 using the same coupon, redemption, and half-year yield; no distinct standard one-step error is identifiable.
CChoice C (541) does not satisfy the equality P4 = 0.93 P8 using the same coupon, redemption, and half-year yield; no distinct standard one-step error is identifiable.
DChoice D (611) does not satisfy the equality P4 = 0.93 P8 using the same coupon, redemption, and half-year yield; no distinct standard one-step error is identifiable.
EChoice E (626) does not satisfy the equality P4 = 0.93 P8 using the same coupon, redemption, and half-year yield; no distinct standard one-step error is identifiable.

Original practice · fully worked

Original variant: shorter-term price discount from two known bond schedules

A bond pays 30 every half-year, redeems 1,000, and yields 4% nominal annually convertible semiannually. Compare otherwise identical six-year and three-year versions. By what percentage is the three-year price lower than the six-year price?

A
4.05%
B
4.27%
C
4.50%
D
4.72%
E
4.95%

Variant answer in brief

The six-year and three-year prices are 1105.75 and 1056.01. Their relative difference is 4.50% of the six-year price, choice C.

Setup

Use the 2% half-year yield to price the twelve-period and six-period cash-flow streams.

P_{12}=30a_{\overline{12}|0.02}+1000v^{12}

P_6=30a_{\overline6|0.02}+1000v^6

Model

Measure the price reduction relative to the longer bond's price.

q=1-\frac{P_6}{P_{12}}

Compute

The prices are 1105.75 and 1056.01, giving reduction 4.4982%.

q=0.04498209

Answer

The three-year price is 4.50% lower, which is choice C.

\boxed{q\approx4.50\%\quad\text{(C)}}

Calculator reproduction

BA II Plus keystrokes

2ND · CLR TVM · 12 · N · 2 · I/Y · 30 · PMT · 1000 · FV · CPT · PVPV = -1105.75
6 · N · CPT · PVPV = -1056.01Keep I/Y, PMT, and FV unchanged.

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Cite this solution

ActuaryProof. “SOA Exam FM Sample Question #239 — 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

All 461 Exam FM sample solutions in syllabus order

Why the other letters tempt

Original variant: shorter-term price discount from two known bond schedules

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