Worked solution · Exam FM
This Exam FM sample reference tests Annuities. An arithmetic perpetuity with first payment 150 and annual increment 10 has value 150/i + 10/i². Setting this equal to 5,000 gives positive root 6.22%, so choice B is correct.
Independent solution
Setup
Decompose the payments into a level perpetuity of 150 and an increasing perpetuity with unit increments scaled by 10.
Model
Multiply by i squared to obtain a quadratic in the positive yield.
Compute
The positive root is i = 6.216991%.
Answer
The annual effective rate is approximately 6.2%, selecting choice B.
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
An annual perpetuity-immediate is priced at 25,000 using a 4% annual effective yield. Its first payment is 500, and every later payment exceeds the preceding payment by K. Calculate K.
The 500 level component is worth 12,500. The remaining 12,500 equals K divided by 4% squared, giving annual increment 20.00, choice C.
Setup
Write the arithmetic perpetuity as a level-payment part plus an increasing part.
Model
Remove the level component and multiply the residual price by the square of the yield.
Compute
The resulting annual increment is 20.0000.
Answer
Each payment increases by 20.00, selecting 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
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