Worked 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.
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30 original Exam FM questions across the syllabus, to be worked in 150 timed minutes, with a full worked solution for each one. Written for Exam FM, not copied from the SOA set. One-time $39 PDF.
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
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