This Exam FM sample reference tests Cash-Flow and Risk Matching. The year-one match gives A + 100B = 1,000; combining it with the 1,783.76 purchase-price equation yields zero redemption A = 915, whose current investment is 915/1.05 = 871, choice C.
These notes identify the calculation error associated with each wrong letter when that error is reproducible.
AChoice A does not satisfy the simultaneous cash-flow and purchase-cost equations; no distinct standard single-step error producing 784 is identifiable.
BChoice B does not satisfy the simultaneous cash-flow and purchase-cost equations; no distinct standard single-step error producing 831 is identifiable.
DThis reports the zero-coupon redemption amount 915 without discounting it one year to its purchase cost.
EChoice E does not satisfy the simultaneous cash-flow and purchase-cost equations; no distinct standard single-step error producing 935 is identifiable.
Original practice · fully worked
Original variant: exact-match cost for a city arts obligation
A city arts office owes 800 in one year and 1,200 in two years. It can buy one-year zeros yielding 4% and two-year notes with 1,000 face, annual coupons 80, and yield 5.5%. Fractional notes are allowed. Find the current cost of an exact match.
A 1,760.00
B 1,810.00
C 1,846.16
D 1,900.00
E 1,950.00
Variant answer in brief
The year-two liability needs 10/9 notes; filling the year-one residual with zeros gives total cost 1,846.16, choice C.
Setup
Setup
The note is the only asset paying at year two, so its quantity is fixed by that liability first.
1080B=1200⟹B=10/9
Model
Model
Its year-one coupons reduce the redemption amount required from one-year zeros.
Z+80B=800⟹Z=711.111
Compute
Compute
Discounting the residual zero and pricing the fractional notes at 5.5% gives 1,846.158.
C=1.04Z+B(1.05580+1.05521080)
Answer
Answer
The exact-match portfolio costs 1,846.16, corresponding to 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.
