Verified solution · Exam FM
This Exam FM sample reference tests Annuities. Treat each five-year interval as one period with effective rate 53.8624%. An arithmetic perpetuity with first payment 2 and increment 10 then has value 2/j + 10/j² = 38.18, choice E.
Independent solution
Setup
Convert the annual yield to the effective rate for each five-year payment interval.
Model
Decompose the arithmetic payment stream into a level perpetuity of 2 and an increasing perpetuity with increment 10.
Compute
The five-year rate is 0.53862395, producing present value 38.182165.
Answer
The perpetuity is worth approximately 38.18, so choice E is correct.
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Original practice · fully worked
A perpetuity pays every three years, beginning with 5 at year 3. Each later payment exceeds the preceding payment by a constant amount K. At a 4% annual effective yield, the perpetuity is priced at 168.32. Calculate K.
The effective three-year rate is 12.4864%. Removing the level-payment component from the quoted price leaves K divided by that rate squared, giving K = 2.00, choice E.
Setup
Convert the annual yield to the effective rate for the three-year payment interval.
Model
Write the arithmetic perpetuity price as a level component plus an increasing component.
Compute
Solving the linear equation gives increment K = 2.0000.
Answer
The payment increment is 2.00, selecting choice E.
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ActuaryProof. “SOA Exam FM Sample Question #238 — Verified Solution.” Verified 2026-07-31.
Source reference: official SOA sample-question PDF. Last reviewed 2026-07-31.
