Worked solution · Exam FM
This Exam FM sample reference tests Duration and Convexity. The annuity present value is 78.1729X and its time-weighted present value is 2,178.3542X; their ratio gives Macaulay duration 27.87 years, choice B.
Independent solution
Setup
Place the first block at times zero through 19 and the second, larger block at times 20 through 49.
Model
Duration requires both ordinary present value and a time-weighted present value; the payment scale X will cancel.
Compute
The two blocks give value factor 78.1729 and time-weighted factor 2,178.3542.
Answer
Their ratio is 27.87 years, corresponding to choice B.
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 subsidy pays 100 at the beginnings of years 1–10 and 300 at the beginnings of years 11–20. At 4% effective annually, calculate its Macaulay duration at time zero.
The 20 dated present-value weights have mean payment time 10.873 years, choice C.
Setup
Beginning-of-year timing places the first subsidy at time zero and the last at time 19.
Model
Discount both tiers and use calendar time, not a restarted index, in the duration numerator.
Compute
The ordinary value is 2,553.1155 and their weighted mean time is 10.87333.
Answer
The Macaulay duration is 10.87 years, which is choice C.
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Drill the method: Exam FM Duration and Convexity problems
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