Verified solution · Exam FM
This Exam FM sample reference tests Annuities and Perpetuities. The first ten due payments contribute 8.10782X and the later 1.5%-growing perpetuity contributes 18.69366X; solving 45,000 = 26.80148X gives X = 1,679, choice A.
Independent solution
Setup
Separate the ten level beginning-of-year payments from the growing tail that starts with the eleventh payment.
Model
The first block is an annuity-due; the tail is a deferred growing perpetuity with growth below the valuation rate.
Compute
Their combined factor is 26.80148, so the stated price implies a level amount of about 1,679.
Answer
The matching listed amount is 1,679, choice A.
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Original practice · fully worked
A foundation pays X immediately and at the next four year-beginnings. Starting at year 5 it pays 1.02X, then increases every later annual payment by 2% forever. At 6% effective, the complete stream is worth 30,000. Find X.
The five level payments plus the year-5 growing tail have factor 24.66349, giving X = 1,216.37, choice C.
Setup
The initial five payments occupy times zero through four; the indexed sequence begins separately at year five.
Model
Value the finite level block directly and the later sequence as a growing perpetuity deferred five years.
Compute
At 6%, the two components combine to 24.663494 times X.
Answer
Dividing 30,000 by that factor gives 1,216.37, which is choice C.
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ActuaryProof. “SOA Exam FM Sample Question #122 — Verified Solution.” Verified 2026-07-31.
Source reference: official SOA sample-question PDF. Last reviewed 2026-07-31.
