Worked solution · Exam FM
This Exam FM sample reference tests Annuities and Perpetuities. The rise to 10, fall to 5, and level tail can be represented by shifted increasing perpetuities; at 9% the resulting factor is 57.83, choice D.
Independent solution
Setup
Start with an indefinitely increasing payment sequence.
Model
Subtract two increasing sequences beginning after the peak to reverse the slope, then add one later sequence to stop the decline at five.
Compute
All three components share the increasing-perpetuity factor and differ only by their shifts.
Answer
The present value is 57.83, nearest choice D.
Test the method on unseen problems
30 original Exam FM questions across the syllabus, to be worked in 150 timed minutes, with a full worked solution for each one. Written for Exam FM, not copied from the SOA set. One-time $39 PDF.
Original practice · fully worked
A perpetuity pays 1, 2, 3, 4, 5, and 6 in years 1 through 6, then pays level amount L from year 7 onward. At 9% effective, its present value is 50. Determine L.
Removing the first six increasing payments leaves a deferred level perpetuity, giving L = 5.35, choice C.
Setup
Value the six explicitly increasing payments first.
Model
At time six, the remaining level payments beginning in year seven form a perpetuity-immediate.
Compute
Solving the residual-value equation gives 5.3465.
Answer
The level tail payment is 5.35, corresponding to choice C.
Keep practicing
These references share syllabus concepts or sit nearby in the official sequence. All 113 Exam FM annuities and non-contingent cash flows practice problems.
Drill the method: Exam FM Annuities and Perpetuities 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.
