Worked solution · Exam FM
This Exam FM sample reference tests Duration and Convexity. With equal payments, payment size cancels from the present-value weights; the seven-payment weighted mean time is 3.62 years, choice E.
Independent solution
Setup
List the seven equal year-end loan payments and discount each at 10%.
Model
Macaulay duration is their present-value-weighted average time; the common payment amount cancels.
Compute
The time-weighted present-value sum is 17.6315 and the annuity present value factor is 4.8684.
Answer
Their ratio is 3.62 years, which corresponds to choice E.
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 contract makes equal payments at each year-end and is valued at 6% effective annually. Its Macaulay duration is 4.613 years. How many payments does the contract make?
A nine-payment annuity at 6% has Macaulay duration 4.6133 years, so the contract makes nine payments, choice C.
Setup
Because payments are equal, test each candidate term using only discounted time weights.
Model
For nine payments, form the time-weighted numerator and the ordinary-annuity denominator.
Compute
The resulting duration is 4.613331 years, matching the stated measure.
Answer
The contract therefore makes nine payments, 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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