Worked solution · Exam FM
This Exam FM sample reference tests Duration and Convexity. The decreasing perpetuity-due has Macaulay duration 0.99 divided by 0.01 plus i; setting this to 12 gives i = 7.25%, and modified duration is 12/1.0725 = 11.19 years, choice C.
Independent solution
Setup
Sum the immediate first payment and the geometric tail to express price as a function of yield.
Model
Differentiating the price gives a compact Macaulay-duration formula; the stated duration determines yield.
Compute
Convert the twelve-year Macaulay duration using the derived 7.25% yield.
Answer
The modified duration is 11.19 years, corresponding to choice C.
Test the method on unseen problems
30 original general cash flows, portfolios, and asset liability management problems with complete solutions and wrong-choice analysis. Written for Exam FM, not copied from the SOA set. One-time $19 PDF.
Original practice · fully worked
A perpetuity-due pays 1 immediately and then decreases by a fixed percentage each year. At 6% effective annually its Macaulay duration is 14 years. Determine the annual percentage decrease.
Solving the geometric-duration relation gives payment ratio 0.989333, hence annual decrease 1.07%, choice C.
Setup
Let q be the ratio of each payment to the preceding payment.
Model
The perpetuity-due Macaulay duration is q divided by the difference between the yield factor and q.
Compute
Solving gives ratio 0.9893333, so the missing fraction is 0.0106667.
Answer
Payments decrease by approximately 1.07% annually, corresponding to choice C.
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These references share syllabus concepts or sit nearby in the official sequence. All 117 Exam FM general cash flows, portfolios, and asset liability management practice problems.
Drill the method: Exam FM Duration and Convexity problems
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