This Exam FM sample reference tests Bond Valuation. Expressing book values after coupons three and four as linear functions of redemption C and setting their difference to the 28.31 amortization gives C = 7,660.15, choice A.
These notes identify the calculation error associated with each wrong letter when that error is reproducible.
BChoice B is inconsistent with the adjacent post-coupon book-value equations; no distinct standard single-step error producing it is identifiable.
CChoice C is inconsistent with the adjacent post-coupon book-value equations; no distinct standard single-step error producing it is identifiable.
DChoice D is inconsistent with the adjacent post-coupon book-value equations; no distinct standard single-step error producing it is identifiable.
EChoice E is inconsistent with the adjacent post-coupon book-value equations; no distinct standard single-step error producing it is identifiable.
Original practice · fully worked
Original variant: one-period premium amortization for a theatre bond
Immediately after a coupon, a theatre bond has book value 2,050. The periodic yield is 3%, and the next coupon is 70. Calculate the premium amortized during the next coupon period.
A 5.00
B 7.00
C 8.50
D 10.00
E 11.50
Variant answer in brief
The next book value is 2,041.50, so book value falls by 8.50, choice C.
Setup
Setup
Accrete the current book value at the periodic yield, then remove the coupon paid at period-end.
BVk+1=2050(1.03)−70=2041.50
Model
Model
Because the bond is at a premium, the post-coupon book value declines and that decline is premium amortization.
amortization=BVk−BVk+1
Compute
Compute
The next book value is 2,041.50, which is 8.50 below the current 2,050.
amortization=2050−2041.50=8.50
Answer
Answer
The premium amortized in the period is 8.50, choice C.
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.
