Verified 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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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.
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ActuaryProof. “SOA Exam FM Sample Question #237 — Verified Solution.” Verified 2026-07-31.
Source reference: official SOA sample-question PDF. Last reviewed 2026-07-31.
