Verified solution · Exam FM
This Exam FM sample reference tests Annuities. Each year's m fractional payments accumulate to 1.0331 at year-end, so annuity X has value 1.0331 times the ten-year annuity factor. Equating it to five biennial payments and using the two-year accumulated-annuity factor 2.075 gives P = 2.1437, choice E.
Independent solution
Setup
Replace each year's fractional payment block by its stated accumulated value 1.0331 at that year-end.
Model
Write the five payments of Y at even years as a five-payment annuity under the two-year rate.
Compute
Equating the geometric sums simplifies P to 1.0331 times the two-year accumulated-annuity factor.
Answer
The biennial payment is approximately 2.14, selecting choice E.
Continue without hunting through PDFs
The searchable 2210-page manual includes this complete solution, its error analysis, and one original worked variant for every active reference.
Error diagnosis
These notes identify the calculation error associated with each wrong letter when that error is reproducible.
Original practice · fully worked
A ten-year annuity pays equal fractions throughout each year. The accumulated value at each year-end of that year's fractional payments is A. An equivalent annuity pays 2.40 at years 2, 4, 6, 8, and 10. The two-year accumulated-annuity factor is 2.10. Calculate A.
The annuity-value cancellation gives the biennial payment equal to A times the two-year accumulated-annuity factor. Therefore A = 2.40/2.10 = 1.1429, choice C.
Setup
Annualize each year's fractional block to amount A at the corresponding year-end.
Model
Equating with the five biennial payments yields the same simplification as grouping the ten years in pairs.
Compute
Using the supplied two-year factor gives A = 1.142857.
Answer
The within-year accumulated amount is 1.1429, selecting choice C.
Keep practicing
These references share syllabus concepts or sit nearby in the official sequence. All 113 Exam FM annuities and non-contingent cash flows practice problems.
Drill the method: Exam FM Annuities and Perpetuities problems
Continue in syllabus order
The 2210-page Financial Mathematics Proof Manual reorganizes 461 verified Exam FM solutions by syllabus skill and adds formula proofs, error patterns, and original worked practice.
ActuaryProof. “SOA Exam FM Sample Question #278 — Verified Solution.” Verified 2026-07-31.
Source reference: official SOA sample-question PDF. Last reviewed 2026-07-31.
