Worked solution · Exam FM
This Exam FM sample reference tests Annuities and Perpetuities. The effective rate per three-year payment period is 22.5043%; the perpetuity-due factor is 5.443595, so X = 735/5.443595 = 135.02, choice A.
Independent solution
Setup
Payments occur every three years beginning immediately, so use a three-year effective rate and a perpetuity-due.
Model
Convert 7% annual effective to the three-year rate before applying the due perpetuity factor.
Compute
The factor is 5.443595, yielding payment 135.02.
Answer
The payment at each three-year boundary is about 135, 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 heritage fund pays X immediately and every four years thereafter forever. At 5% effective annually, the fund is worth 1,000. Determine X.
The four-year perpetuity-due factor gives X = 177.30, choice C.
Setup
Convert the annual rate to the effective rate over each four-year payment interval.
Model
Immediate payment timing makes the stream a perpetuity-due on that interval scale.
Compute
Multiplying value by j divided by one plus j gives 177.2975.
Answer
Each quadrennial grant is 177.30, 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
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