Worked solution · Exam FM
This Exam FM sample reference tests Annuities and Perpetuities. The first ten due payments contribute 8.10782X and the later 1.5%-growing perpetuity contributes 18.69366X; solving 45,000 = 26.80148X gives X = 1,679, choice A.
Independent solution
Setup
Separate the ten level beginning-of-year payments from the growing tail that starts with the eleventh payment.
Model
The first block is an annuity-due; the tail is a deferred growing perpetuity with growth below the valuation rate.
Compute
Their combined factor is 26.80148, so the stated price implies a level amount of about 1,679.
Answer
The matching listed amount is 1,679, choice A.
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 foundation pays X immediately and at the next four year-beginnings. Starting at year 5 it pays 1.02X, then increases every later annual payment by 2% forever. At 6% effective, the complete stream is worth 30,000. Find X.
The five level payments plus the year-5 growing tail have factor 24.66349, giving X = 1,216.37, choice C.
Setup
The initial five payments occupy times zero through four; the indexed sequence begins separately at year five.
Model
Value the finite level block directly and the later sequence as a growing perpetuity deferred five years.
Compute
At 6%, the two components combine to 24.663494 times X.
Answer
Dividing 30,000 by that factor gives 1,216.37, which is 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
Keep studying
Work through the related free solutions for this topic, review the formulas you used, or keep every current Exam FM solution in one searchable PDF.
