Worked solution · Exam FM
This Exam FM sample reference tests Annuities. Payments at years 5 through 10 are discounted at 1%, while the remaining perpetuity is valued at time 10 using 5% and then discounted through the first regime. The total factor is 23.675078, giving X = 4223.85 and choice B.
Independent solution
Setup
Separate the six payments at times 5 through 10 from the payments beginning at time 11.
Model
At time 10, payments from year 11 onward form a perpetuity-immediate at 5%.
Compute
The combined present-value factor is 23.67507807, so X = 4223.8509.
Answer
The annual perpetuity payment is approximately 4,224, which is choice B.
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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 pays 3,000 annually beginning at year 3. Interest is 2% annually through year 5 and a constant rate j thereafter. Its present value is 62659.54. Calculate j.
Remove the year-3 through year-5 payments from the quoted value. Accumulating the residual to time 5 gives the value of a 3,000 perpetuity, so j = 5.00%, choice A.
Setup
Discount the three payments occurring under the 2% regime separately.
Model
The residual price is the discounted time-5 value of payments beginning at year 6.
Compute
Solving the tail-value equation gives long-run rate 5.0000%.
Answer
The later annual rate is 5.00%, selecting choice A.
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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