Worked solution · Exam FM
This Exam FM sample reference tests Annuities and Perpetuities. Writing the payments as a level perpetuity of 4 plus twice an increasing perpetuity gives 4/0.06 + 2(1.06)/0.06² = 655.56, choice B.
Independent solution
Setup
Separate each payment into a constant four-unit layer plus twice the sequence one, two, three, and so on.
Model
The first layer is a level perpetuity-immediate and the second is a scaled increasing perpetuity-immediate.
Compute
Applying the two closed forms at 6% produces 66.67 plus 588.89, totaling 655.56.
Answer
The required present value is approximately 656, which is choice B.
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 district pays 10 at the end of year 1, 13 at the end of year 2, 16 at the end of year 3, and continues increasing by 3 each year forever. At 5% effective, find the present value.
A level perpetuity of 10 plus a three-unit arithmetic increase has value 1,400, choice C.
Setup
Retain the first-payment level of ten and isolate the three-unit step that begins with the second payment.
Model
The step component has discounted value one over i squared for each unit of annual increase.
Compute
At 5%, the level layer is 200 and the growth layer is 1,200.
Answer
Their sum is 1,400, which appears in 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.
