Worked solution · Exam FM
This Exam FM sample reference tests Annuities. Value the first ten level payments of k, then at time 10 value a perpetuity beginning with k + 200 and increasing by 200 annually. Solving the linear 50,000 price equation gives k = 162.83, so choice C is correct.
Independent solution
Setup
Separate the first ten level payments from the increasing perpetuity beginning with payment 11.
Model
At time 10, value the tail as a level perpetuity beginning at k + 200 plus an arithmetic-increase perpetuity.
Compute
Discounting the tail ten years and solving gives k = 162.834657.
Answer
The first ten payments are approximately 163, selecting choice C.
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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-immediate pays 500 in each of years 1 through 8. Beginning with year 9, every payment is D larger than the previous payment. At a 6% annual yield, the price is 17570.24. Calculate D.
Value the first eight payments separately and express the time-8 increasing perpetuity in terms of D. Solving the quoted price gives annual increment 50.00, choice D.
Setup
Value the first eight level payments at 6%.
Model
At time 8, the tail begins with 500 + D and increases by D forever.
Compute
Solving the quoted price equation gives D = 50.000000.
Answer
The perpetual annual increment is 50.00, selecting choice D.
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
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