Worked solution · Exam FM
This Exam FM sample reference tests Annuities. A geometrically decreasing perpetuity has price 1,000 divided by 0.057 + r/100. Setting this equal to 16,000 gives r = 0.5500%, so choice B is correct.
Independent solution
Setup
A decrease of r percent is a geometric growth rate of negative r divided by 100.
Model
Apply the growing-perpetuity-immediate price formula.
Compute
Solving the denominator equation gives r = 0.550000%.
Answer
The annual payment decrease is approximately 0.55%, selecting 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
An environmental reserve costs 25,000 and pays annually forever. Payments decline by 1% each year, and the annual effective yield is 4%. Calculate the first year-end payment.
A 1% decline is growth rate −1%, so the perpetuity denominator is 4% − (−1%) = 5%. Multiplying 25,000 by 5% gives first payment 1,250.00, choice A.
Setup
Represent the annual decline as geometric growth rate negative 1%.
Model
Use the growing-perpetuity-immediate price formula and solve for the first payment.
Compute
The first payment is 25,000 times 0.05, or 1250.00.
Answer
The first payment is 1,250.00, 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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