Verified solution · Exam FM
This Exam FM sample reference tests Annuities and Perpetuities. Fund K receives 1,000 principal plus a decreasing interest stream 1,300, 1,235, …, 65; accumulating both parts at 8.25% gives 86,902, choice D.
Independent solution
Setup
Fund J loses 1,000 of principal each year, so its annual interest withdrawals decline by 65.
Model
Each transfer to Fund K consists of the level 1,000 principal withdrawal plus the arithmetic decreasing interest component.
Compute
Accumulating the level and decreasing sequences at 8.25% gives a total of 86,902.
Answer
The year-20 value of Fund K is 86,902, corresponding to choice D.
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Original practice · fully worked
A park reserve begins at 10,000 and earns 5%. At each year-end for ten years it withdraws that year's interest plus 500, leaving the reserve lower by 500. Each withdrawal is deposited into a second fund earning 7%. Find the second fund at year 10.
The transfers decline from 1,000 to 775; accumulating them at 7% gives 12,453.43, choice C.
Setup
Before transfer k, the source principal has fallen by 500 for each prior year.
Model
That makes total transfers an arithmetic sequence beginning at 1,000 and decreasing by 25.
Compute
Accumulating each transfer from its deposit date to year ten gives 12,453.4308.
Answer
The second fund holds 12,453.43, which is choice C.
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ActuaryProof. “SOA Exam FM Sample Question #170 — Verified Solution.” Verified 2026-07-31.
Source reference: official SOA sample-question PDF. Last reviewed 2026-07-31.
