This Exam FM sample reference tests Full Immunization. The requested ratio is B/b = 2,807.12, or 2,807. The result agrees with the published answer key, choice A.
These notes identify the calculation error associated with each wrong letter when that error is reproducible.
BChoice B (2873) does not match the checked full immunization result (2807); no distinct standard one-step error is identifiable.
CChoice C (2902) does not match the checked full immunization result (2807); no distinct standard one-step error is identifiable.
DChoice D (2976) does not match the checked full immunization result (2807); no distinct standard one-step error is identifiable.
EChoice E (3019) does not match the checked full immunization result (2807); no distinct standard one-step error is identifiable.
Original practice · fully worked
Original variant: unknown zero maturity from a duration budget
A liability portfolio has current value 5,000 and Macaulay duration 4. An immunizing asset portfolio holds a time-1 zero-coupon asset worth 1,200 today and one additional zero worth 3,800 today. Find the maturity of the second zero.
A 4.21 years
B 4.53 years
C 4.95 years
D 5.26 years
E 5.67 years
Variant answer in brief
Solving 1,200 + 3,800b = 20,000 gives b = 4.9474 years. The maturity is 4.95 years, so choice C is correct.
Setup
Setup
Present value is already matched, so only the dollar-duration equation is needed to determine the second zero’s maturity.
PVA=1200+3800=5000
Model
Model
For zero-coupon assets, Macaulay duration equals maturity; weight each maturity by its current market value.
1(1200)+b(3800)=4(5000)
Compute
Compute
Solving 1,200 + 3,800b = 20,000 gives b = 4.9474 years.
b=380020000−1200=4.947368
Answer
Answer
The maturity is 4.95 years, so choice C is correct.
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.
