Worked solution · Exam FM
This Exam FM sample reference tests Duration and Convexity. For level payments the payment amount cancels from the duration ratio; at 6%, the ten-payment present-value-weighted mean time is 5.022 years, choice B.
Independent solution
Setup
List the ten equal end-of-year mortgage payments and discount them at 6%.
Model
The common payment cancels from the time-weighted present-value ratio.
Compute
The increasing-annuity numerator divided by the ordinary-annuity denominator is 5.02201.
Answer
The mortgage Macaulay duration is 5.02 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 level annual-payment mortgage is valued at 6% effective. Its Macaulay duration is 5.022 years. How many year-end payments does it have?
At 6%, a ten-payment annuity has Macaulay duration 5.022 years, so the term is ten payments, choice C.
Setup
Evaluate candidate level-payment terms using discounted time weights.
Model
Ten payments produce duration 5.022007 years.
Compute
The adjacent nine- and eleven-payment terms bracket the observed duration.
Answer
The mortgage has ten 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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