Verified solution · Exam FM

SOA Exam FM Sample Question #417 Solution

This Exam FM sample reference tests Bond Valuation. The desired 6% yield exceeds the 5% coupon rate, so the investor's adverse redemption is the latest possible date, maturity; the callable bond's protected price therefore equals the non-callable price 4,361, choice D.

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

Compare the coupon rate with the investor's required yield.

c=5\%<y=6\%\Longrightarrow\text{discount bond}

Model

For a discount bond, delaying redemption keeps below-market coupons outstanding longer and lowers value.

P_k=250a_{\overline{k}|\,0.06}+5000(1.06)^{-k}

Compute

The latest allowable redemption is ordinary maturity, identical to the non-callable bond's cash flow.

P_k\ \text{decreases as }k\text{ increases}

Answer

The maximum protected price is therefore 4,361, corresponding to choice D.

\boxed{P_{\max}=P_n=4361\quad\text{(D)}}

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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 discount-bond call-date price ordering; no distinct standard single-step error producing it is identifiable.
BChoice B is inconsistent with the discount-bond call-date price ordering; no distinct standard single-step error producing it is identifiable.
CChoice C is inconsistent with the discount-bond call-date price ordering; no distinct standard single-step error producing it is identifiable.
EChoice E is inconsistent with the discount-bond call-date price ordering; no distinct standard single-step error producing it is identifiable.

Original practice · fully worked

Original variant: effect of callability on protected price for a discount bond

A bond's coupon rate is below an investor's required yield. It is callable at par on several dates through maturity and is otherwise identical to a non-callable bond. How does its maximum price guaranteeing the required yield compare with the non-callable bond's price?

A
It must be at least 10% lower
B
It must be slightly lower
C
It depends only on face amount
D
It is equal
E
It is higher

Variant answer in brief

For a discount bond the latest redemption is adverse, and maturity is available; that cash flow is the non-callable bond, so protected prices are equal, choice D.

Setup

Below-market coupons make longer time to redemption worse for the buyer at the required yield.

c<y\Longrightarrow P_k\downarrow\text{ as }k\uparrow

Model

Maturity is the latest permitted redemption and therefore sets the protected price.

k_{\mathrm{worst}}=n

Compute

At maturity the callable and non-callable cash-flow streams are identical.

CF_{\mathrm{callable},n}=CF_{\mathrm{noncallable}}

Answer

Their protected and market prices are equal, corresponding to choice D.

\boxed{P_{\max,\mathrm{callable}}=P_{\mathrm{noncallable}}\quad\text{(D)}}

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ActuaryProof. “SOA Exam FM Sample Question #417 — 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: effect of callability on protected price for a discount bond

Variant answer in brief

Setup

Model

Compute

Answer

Related Exam FM solutions

Turn this solution into a complete study sequence

Cite this solution