Verified solution · Exam FM
This Exam FM sample reference tests Annuities. The ten payments form a finite geometric stream with payment growth 15% and discount rate 5%. Direct valuation gives 1483.62, so choice E is correct.
Independent solution
Setup
Payment k is the first payment grown by 15% for k minus 1 years.
Model
Discount the ten-term geometric stream at 5%.
Compute
Evaluating the finite geometric sum gives 1483.621512.
Answer
The annuity present value is approximately 1,484, so choice E is correct.
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Original practice · fully worked
A six-payment annuity pays 500 at year 1, and each later payment grows by the same annual rate g. At a 4% annual yield, its present value is 2816.16. Calculate g.
Equating the six-term geometric payment stream to the quoted price and solving for its common growth rate gives 3.00%, choice D.
Setup
Write all six payments from the unknown common growth rate.
Model
Set their discounted value at 4% equal to the quoted price.
Compute
The economically relevant root is g = 3.0000%.
Answer
The annual payment growth rate is 3.00%, selecting choice D.
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ActuaryProof. “SOA Exam FM Sample Question #245 — Verified Solution.” Verified 2026-07-31.
Source reference: official SOA sample-question PDF. Last reviewed 2026-07-31.
