Worked solution · Exam FM
This Exam FM sample reference tests Annuities. The first 30 due payments grow 3% and are discounted at 7%. From payment 31 onward the level amount equals payment 30. The finite block plus the time-29 level-perpetuity value totals 8033.38, so choice E is correct.
Independent solution
Setup
Value payments 1 through 30 at times 0 through 29 as a growing annuity-due.
Model
At time 29, the future level perpetuity begins one year later with amount equal to payment 30.
Compute
The finite segment and tail sum to 8033.377503.
Answer
The perpetuity-due price is approximately 8,033, 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 perpetuity-due pays 200 immediately. Payments grow at rate g through payment 10, and every payment from number 11 onward remains equal to payment 10. At a 6% annual yield, the price is 4050.31. Calculate g.
Valuing the first ten due payments and the level tail as functions of g, then solving the quoted price, gives growth rate 2.00%, choice B.
Setup
Value the first ten due payments under the unknown growth rate.
Model
At time 9, append the level perpetuity beginning one year later at payment-10 amount.
Compute
Solving PV1 plus PV2 equal to the quoted price gives g = 2.000000%.
Answer
The early payment growth rate is 2.00%, selecting choice B.
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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