This Exam FM sample reference tests Duration and Convexity. The first duration equation has the unique positive solution v = 0.9; using that discount factor for the four-payment annuity gives duration 1.369, choice B.
These notes identify the calculation error associated with each wrong letter when that error is reproducible.
AChoice A is inconsistent with the two duration ratios with time-zero payments included; no distinct standard single-step error producing it is identifiable.
CChoice C is inconsistent with the two duration ratios with time-zero payments included; no distinct standard single-step error producing it is identifiable.
DChoice D is inconsistent with the two duration ratios with time-zero payments included; no distinct standard single-step error producing it is identifiable.
EChoice E is inconsistent with the two duration ratios with time-zero payments included; no distinct standard single-step error producing it is identifiable.
Original practice · fully worked
Original variant: duration of community-theatre royalty stream
A community-theatre royalty stream pays 90 at year 0, 60 at year 2, 140 at year 5. The valuation rate is 5.5% effective annually. Determine the Macaulay duration of these promised cash flows.
A 2.113
B 2.363
C 2.563
D 2.813
E 3.113
Variant answer in brief
Discounted time weights give a Macaulay duration of 2.563 years, choice C.
Setup
Setup
Place each promised amount at its payment year and use the same annual discount factor for every term.
v=(1+0.0550)−1
Model
Model
Macaulay duration is the present-value-weighted average payment time.
DM=∑tCtvt∑ttCtvt
Compute
Compute
The denominator is the cash-flow present value; dividing the time-weighted numerator by it gives 2.563.
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.
