Worked solution · Exam FM
This Exam FM sample reference tests Duration and Convexity. The zero's modified duration gives yield 7.991%; at that yield the ten level payments have a present-value-weighted mean time of 4.872 years, choice D.
Independent solution
Setup
A ten-year zero has Macaulay duration ten, so its modified duration identifies the yield.
Model
Use that yield to discount the ten annual annuity payments.
Compute
The ratio of the time-weighted sum to the ordinary present-value sum is 4.87195.
Answer
The annuity Macaulay duration is 4.87 years, corresponding to choice D.
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
An eight-year zero-coupon security has modified duration 7.40 years. Determine its annual effective yield.
An eight-year zero has Macaulay duration 8, so 8/7.40 minus one gives yield 8.11%, choice C.
Setup
The only payment occurs in year eight, making Macaulay duration exactly eight.
Model
Convert that Macaulay duration to the observed modified duration.
Compute
Solving the one-step equation gives 0.0810811.
Answer
The annual effective yield is 8.11%, corresponding to choice C.
Keep practicing
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
Keep studying
Work through the related free solutions for this topic, review the formulas you used, or keep every current Exam FM solution in one searchable PDF.
