Verified solution · Exam FM

SOA Exam FM Sample Question #264 Solution

This Exam FM sample reference tests Bond Pricing and Yields. The annual-payment bond price implies coupon X = 10.49. The equivalent half-year yield is 4.8809%; pricing twenty coupons of X/2 gives P = 451.57, 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 Pricing and Yields question

Setup

Solve the first bond's ten-year annual price equation for its annual coupon.

450=Xa_{\overline{10}|0.10}+1000(1.10)^{-10}

Model

Convert the 10% annual effective yield to an equivalent half-year rate for the second bond.

j=(1.10)^{1/2}-1

Compute

The annual coupon is 10.4900 and the half-year rate is 4.880885%. The second price is 451.5730.

P=\frac{X}{2}a_{\overline{20}|j}+1000(1+j)^{-20}

P=451.57302890

Answer

The second bond's price is approximately 452, selecting choice C.

\boxed{P\approx452\quad\text{(C)}}

Calculator reproduction

BA II Plus keystrokes

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

2ND · CLR TVM · 10 · N · 10 · I/Y · 450 · +/- · PV · 1000 · FV · CPT · PMTPMT = 10.49
20 · N · 4.880885 · I/Y · 5.245016 · PMT · 1000 · FV · CPT · PVPV = -451.57

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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 (439) does not satisfy the annual-coupon calibration followed by equivalent half-year bond pricing; no distinct standard one-step error is identifiable.
BChoice B (442) does not satisfy the annual-coupon calibration followed by equivalent half-year bond pricing; no distinct standard one-step error is identifiable.
DChoice D (457) does not satisfy the annual-coupon calibration followed by equivalent half-year bond pricing; no distinct standard one-step error is identifiable.
EChoice E (461) does not satisfy the annual-coupon calibration followed by equivalent half-year bond pricing; no distinct standard one-step error is identifiable.

Original practice · fully worked

Original variant: annual coupon total recovered from a semiannual bond price

A six-year 1,000-redemption bond pays equal semiannual coupons and is priced at 950. Its yield is 8% annual effective. Calculate twice the semiannual coupon, interpreted as the bond's annual coupon total.

A
67.85
B
71.25
C
74.64
D
78.03
E
81.42

Variant answer in brief

Convert 8% annual effective to a half-year rate and solve the twelve-period price equation. The half-year coupon is 33.93, so the annual coupon total is 67.85, choice A.

Setup

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

j=(1.08)^{1/2}-1

Model

Solve the twelve-period bond price for the half-year coupon C.

950=Ca_{\overline{12}|j}+1000(1+j)^{-12}

Compute

The half-year coupon is 33.9266, so twice that amount is 67.8533.

2C=67.85327231

Answer

The annual coupon total is 67.85, selecting choice A.

\boxed{2C\approx67.85\quad\text{(A)}}

Calculator reproduction

BA II Plus keystrokes

2ND · CLR TVM · 12 · N · 3.923048 · I/Y · 950 · +/- · PV · 1000 · FV · CPT · PMTPMT = 33.93

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Cite this solution

ActuaryProof. “SOA Exam FM Sample Question #264 — 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: annual coupon total recovered from a semiannual bond price

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