Worked solution · Exam FM
This Exam FM sample reference tests Annuities and Perpetuities. The increasing stream begins immediately, so shifting the standard increasing annuity one period earlier gives value (1.05)² divided by 0.05² = 441, choice D.
Independent solution
Setup
Index the immediate payment of one at time zero and subsequent payments two, three, and so on.
Model
The generating function for this increasing geometric-weighted sequence is one divided by one minus v squared.
Compute
Replace one minus v by i divided by one plus i.
Answer
The present value is 441, corresponding to choice D.
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 perpetuity-immediate pays 1 after one year, 2 after two years, and continues increasing by one each year. Its present value is 110. Determine the annual effective interest rate.
The increasing perpetuity-immediate value is one plus i divided by i squared; setting it to 110 gives i = 10%, choice C.
Setup
Use the standard value of an increasing perpetuity whose first payment is in year one.
Model
Rearrange the value equation into a quadratic in the positive annual rate.
Compute
The positive root is 0.10; the other root is economically inadmissible.
Answer
The annual effective rate is 10.00%, 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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