Worked solution · Exam FM
This Exam FM sample reference tests Annuities and Perpetuities. On a half-year scale the immediate perpetuity-due value is 1 + 1/j = 23, so j = 1/22; compounding that half-year rate twice gives annual effective rate 9.3%, choice E.
Independent solution
Setup
Use six months as one payment and interest period.
Model
The first unit is paid immediately, so the stream is a perpetuity-due.
Compute
Its value determines the half-year rate; two such factors produce the annual effective rate.
Answer
The annual effective rate is approximately 9.3%, corresponding to choice E.
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
Payments of 1 occur every six months forever, beginning immediately. The annual effective interest rate is 10.25%. Determine the present value.
The equivalent half-year rate is 5%, so the semiannual perpetuity-due value is 21, choice C.
Setup
Convert the annual effective accumulation factor to one half-year.
Model
The square root gives a 5% effective rate per payment period.
Compute
An immediate first payment makes the perpetuity value one plus one over the rate.
Answer
The present value is 21, corresponding to 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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