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.
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.
Variant answer in brief
A discount is the excess of redemption value over purchase price. Thus the purchase price must be below the redemption value, choice A.
Setup
Setup
Let P denote purchase price and C denote the contractual redemption payment.
discount=C−P
Model
Model
Calling the purchase a discount means this difference is positive.
C−P>0
Compute
Compute
Rearrange the defining inequality without making any assumption about face amount.
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.
