Worked solution · Exam FM
This Exam FM sample reference tests Duration and Convexity. The discounted liability cash flows total 66.57, and their time-weighted present values total 226.45. Their ratio is 3.40 years, so choice C is correct.
Independent solution
Setup
Discount each liability amount at 8% and retain its payment time for the duration numerator.
Model
Macaulay duration is the time-weighted present value divided by total present value.
Compute
The present value is 66.5729 and the weighted total is 226.4477, giving duration 3.401500 years.
Answer
The liability duration is approximately 3.4 years, selecting 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 liability pays 100 at year 1, 200 at year 3, and X at year 5. Values are discounted at 5% annually. Determine X if the liability's Macaulay duration must equal 3.5 years.
Setting the time-weighted present value equal to 3.5 times total present value and isolating the year-5 amount gives X = 276.08, choice E.
Setup
Write the present-value and duration-numerator contributions of the three liabilities.
Model
Impose the target duration by setting the numerator equal to 3.5 times present value.
Compute
At 5%, solving the resulting linear equation gives X = 276.08.
Answer
The final liability must be 276.08, which is choice E.
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
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