Verified solution · Exam FM

SOA Exam FM Sample Question #416 Solution

This Exam FM sample reference tests Bond Valuation. Coupon amount is 500i, so Bond A's price simplifies to 500(1 + vᵐ) = 800 and vᵐ = 0.6; Bond B then costs 500(1 + 0.6³) = 608, 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

The coupon rate is half the yield, making the annual coupon amount 500 times i.

800=500i\,a_{\overline{m}|\,i}+1000v^m=500(1+v^m)

Model

Use i times the annuity factor equals one minus the terminal discount factor to simplify Bond A's price.

v^m=0.6

Compute

The derived m-year discount factor is 0.6; cube it for Bond B's three-times-longer term.

P_B=500i\,a_{\overline{3m}|\,i}+1000v^{3m}=500(1+v^{3m})

Answer

Bond B's price is 608, corresponding to choice C.

\boxed{P_B=500(1+0.6^3)=608\quad\text{(C)}}

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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 half-yield coupon bond price identities; no distinct standard single-step error producing it is identifiable.
BChoice B is inconsistent with the half-yield coupon bond price identities; no distinct standard single-step error producing it is identifiable.
DChoice D is inconsistent with the half-yield coupon bond price identities; no distinct standard single-step error producing it is identifiable.
EChoice E is inconsistent with the half-yield coupon bond price identities; no distinct standard single-step error producing it is identifiable.

Original practice · fully worked

Original variant: terminal discount factor from a coupon-yield relation

An m-year face-1,000 bond has price 800 and annual coupon rate equal to half its annual effective yield. Determine the discount factor through maturity.

A
0.40
B
0.50
C
0.60
D
0.70
E
0.80

Variant answer in brief

The coupon-yield relation reduces price to 500(1 + vᵐ); setting this to 800 gives vᵐ = 0.60, choice C.

Setup

Translate the coupon-rate condition into annual coupon amount 500i.

800=500i\,a_{\overline{m}|\,i}+1000v^m

Model

Replace i times the annuity factor by one minus the maturity discount factor.

800=500(1-v^m)+1000v^m

Compute

The bond-price equation becomes linear in that factor.

800=500+500v^m\Longrightarrow v^m=0.60

Answer

The discount factor through maturity is 0.60, corresponding to choice C.

\boxed{v^m=0.60\quad\text{(C)}}

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Cite this solution

ActuaryProof. “SOA Exam FM Sample Question #416 — 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

All 461 Exam FM sample solutions in syllabus order

Why the other letters tempt

Original variant: terminal discount factor from a coupon-yield relation

Variant answer in brief

Setup

Model

Compute

Answer

Related Exam FM solutions

Turn this solution into a complete study sequence

Cite this solution