Worked solution · Exam FM

SOA Exam FM Sample Question #421 Solution

This Exam FM sample reference tests Premium Bond Value Relationships. A bond is purchased at a premium precisely when its purchase price exceeds its redemption value. Therefore E is the statement that must hold.

Independent analysis by ActuaryProof · reviewed October 6, 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 Premium Bond Value Relationships question

Setup

Use the bond-pricing meaning of premium rather than comparing the coupon rate with an unspecified face amount.

\text{premium}=P-C

Model

Here P is the purchase price and C is the amount paid at redemption. A premium purchase requires a positive premium.

P-C>0

Compute

The inequality immediately gives the required ordering. No ordering involving face amount follows without additional terms.

P>C

Answer

Only choice E states that the purchase price exceeds the redemption value.

\boxed{P>C\quad\text{(E)}}

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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 compares face amount with price, but a nonstandard redemption amount can break that ordering.
BChoice B reverses the defining premium inequality between redemption value and purchase price.
CChoice C asserts an ordering between redemption and face amounts that the premium condition does not determine.
DChoice D also concerns face amount versus redemption value, which is independent of whether the bond was bought at a premium.

Original practice · fully worked

Original variant: identify the necessary discount relation

A municipal bond is purchased at a discount and will be held until its contractual redemption date. Its face amount and redemption value are not assumed to be equal. Which relationship must hold solely because the purchase is described as being at a discount?

A
Purchase price is less than redemption value.
B
Purchase price is greater than face amount.
C
Face amount is less than redemption value.
D
Coupon rate is greater than yield rate.
E
Face amount equals purchase price.

Answer and calculation

A discount is the excess of redemption value over purchase price. Thus the purchase price must be below the redemption value, choice A.

Setup

Let P denote purchase price and C denote the contractual redemption payment.

\text{discount}=C-P

Model

Calling the purchase a discount means this difference is positive.

C-P>0

Compute

Rearrange the defining inequality without making any assumption about face amount.

P<C

Answer

Choice A is the only necessary relationship.

\boxed{P<C\quad\text{(A)}}

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How to solve this Premium Bond Value Relationships question

Setup

Model

Compute

Answer

Financial Mathematics Bonds Practice Workbook

Why the other letters tempt

Original variant: identify the necessary discount relation

Answer and calculation

Setup

Model

Compute

Answer

Related Exam FM solutions

Next steps for Exam FM Bonds