Worked solution · Exam FM
This Exam FM sample reference tests Annuities and Perpetuities. Equating the accumulated n-year annuity to the n-year-spaced perpetuity gives (1.109ⁿ − 1)² = 96.04; therefore the common value is X = 1,960, choice C.
Independent solution
Setup
Express both values through the same n-year accumulation excess, one plus i to n minus one.
Model
The finite annuity accumulation is proportional to that excess, while the spaced perpetuity value is inversely proportional to it.
Compute
Equating the two produces a square equation with positive root 9.8.
Answer
Substitution into either value expression gives 1,960, which is choice C.
Test the method on unseen problems
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 cooperative saves 30 at each year-end for N years at 8%. A separate legacy pays 500 at the end of every N-year block forever. The accumulated savings at year N equal the legacy's present value today. Find that common value.
Writing both quantities in terms of q = 1.08ᴺ − 1 gives q² = 4/3 and common value 433.01, choice C.
Setup
Let q denote the growth above one over the N-year block, which appears in both streams.
Model
The savings accumulation is linear in q, whereas the block-payment perpetuity value is 500 divided by q.
Compute
Equating them gives q squared equal to four-thirds and therefore X = 433.0127.
Answer
The two independently valued streams meet at 433.01, 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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