Verified solution · Exam FM
This Exam FM sample reference tests Annuities. Equating the 20-year 1,000 annuity to a perpetuity paying 600 for ten years then 1,200 reduces to a quadratic in the ten-year discount factor. The valid root is 0.4, giving rate 9.5958% and common value 8753.81, choice B.
Independent solution
Setup
Write the first annuity value and decompose the stepped perpetuity into 600 forever plus an extra 600 beginning at year 11.
Model
Set x equal to the ten-year discount factor and simplify the equality.
Compute
The implied annual rate is 9.595823%, and the common present value is 8753.8091.
Answer
The common value is approximately 8,750, so choice B is correct.
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Original practice · fully worked
At a 6% annual yield, a 15-year annuity pays 1,000 each year. A second stream pays 500 in each of years 1 through 5 and then pays Y annually forever beginning in year 6. Calculate Y so the two streams have equal present value.
The 15-year annuity value minus the first five 500 payments is the time-0 value of the deferred Y perpetuity. Moving that residual to time 5 and multiplying by 6% gives Y = 610.72, choice A.
Setup
Value the finite 15-year annuity and the first five payments of the stepped stream.
Model
The residual present value is a perpetuity-immediate valued at time 5 and discounted back five years.
Compute
Solving gives later annual payment 610.72.
Answer
The later perpetuity payment is 610.72, selecting choice A.
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ActuaryProof. “SOA Exam FM Sample Question #253 — Verified Solution.” Verified 2026-07-31.
Source reference: official SOA sample-question PDF. Last reviewed 2026-07-31.
