Verified solution · Exam FM

SOA Exam FM Sample Question #248 Solution

This Exam FM sample reference tests Bond Pricing and Yields. Kate's purchase price implies half-year yield 3.7155%, giving book value 917.19 after one year. Wallace's 5% half-year yield gives discount 161.58. Their difference is 755.61, so choice C 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

Recover Kate's half-year yield from her 900 purchase price, ten coupons of 25, and 1,000 redemption.

900=25a_{\overline{10}|j}+1000(1+j)^{-10}

Model

At the one-year date, value Kate's eight remaining periods at her yield and Wallace's eight periods at his 5% half-year yield.

B=25a_{\overline8|j}+1000(1+j)^{-8}

D=1000-\left[25a_{\overline8|0.05}+1000(1.05)^{-8}\right]

Compute

The values are B = 917.19 and D = 161.58, so B − D = 755.61.

B-D=755.61244914

Answer

The requested difference is approximately 756, selecting choice C.

\boxed{B-D\approx756\quad\text{(C)}}

Calculator reproduction

BA II Plus keystrokes

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

2ND · CLR TVM · 10 · N · 900 · +/- · PV · 25 · PMT · 1000 · FV · CPT · I/YI/Y = 3.7155
8 · N · 3.715511 · I/Y · CPT · PVPV = -917.19
8 · N · 5 · I/Y · CPT · PVPV = -838.42

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.

AChoice A (724) does not satisfy the two separate eight-period bond valuations after recovering Kate's purchase yield; no distinct standard one-step error is identifiable.
BChoice B (738) does not satisfy the two separate eight-period bond valuations after recovering Kate's purchase yield; no distinct standard one-step error is identifiable.
DChoice D (838) does not satisfy the two separate eight-period bond valuations after recovering Kate's purchase yield; no distinct standard one-step error is identifiable.
EChoice E (917) does not satisfy the two separate eight-period bond valuations after recovering Kate's purchase yield; no distinct standard one-step error is identifiable.

Original practice · fully worked

Original variant: original bond price recovered from a later book value

A five-year bond pays 40 annually and redeems 1,000. Immediately after the second coupon, its book value at the original constant yield is 970. Calculate the bond's original purchase price.

A
809.50
B
857.11
C
904.73
D
952.35
E
999.97

Variant answer in brief

The time-2 book value prices the three remaining coupons and redemption, implying yield 5.1038%. Pricing all five original cash flows at that yield gives 952.35, choice D.

Setup

Use the time-2 book value to recover the constant annual yield from the three remaining payments.

970=40a_{\overline3|j}+1000(1+j)^{-3}

Model

Apply that same yield to the original five-payment cash-flow stream.

P_0=40a_{\overline5|j}+1000(1+j)^{-5}

Compute

The recovered yield is 5.103768%, and the original price is 952.35.

P_0=952.34937261

Answer

The original purchase price was 952.35, selecting choice D.

\boxed{P_0\approx952.35\quad\text{(D)}}

Calculator reproduction

BA II Plus keystrokes

2ND · CLR TVM · 3 · N · 970 · +/- · PV · 40 · PMT · 1000 · FV · CPT · I/YI/Y = 5.1038
5 · N · CPT · PVPV = -952.35

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 #248 — 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: original bond price recovered from a later book value

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