Verified solution · Exam FM
This Exam FM sample reference tests Annuities and Perpetuities. Company Q accumulates to 84.7009X; Company R's principal and separately reinvested interest total 7,911.91, so X = 93.41, choice D.
Independent solution
Setup
Company Q's deposits remain together at 9%, forming a standard accumulated annuity.
Model
For Company R, the 2,500 principal deposits are retained while each year's 9% interest is reinvested separately at 8%.
Compute
The two R components total 7,911.91; equating this to Q's value gives X = 93.41.
Answer
The annual Q deposit is 93.41, which is choice D.
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Original practice · fully worked
A library deposits 100 at the beginning of each year for ten years. Principal remains uncredited, but at each year-end the accumulated principal earns 5%; that interest is moved to a separate account earning 3% until year 10. Find total value at year 10.
Principal totals 1,000 and the ten interest transfers accumulate to 301.30, giving 1,301.30, choice C.
Setup
At year k the source principal is 100k, so its transferred interest is 5k.
Model
Each interest transfer then grows in the separate 3% account for the remaining years.
Compute
Those transfers accumulate to 301.2993, while principal itself totals 1,000.
Answer
The combined year-ten value is 1,301.30, corresponding to choice C.
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ActuaryProof. “SOA Exam FM Sample Question #171 — Verified Solution.” Verified 2026-07-31.
Source reference: official SOA sample-question PDF. Last reviewed 2026-07-31.
