Worked solution · Exam FM
This Exam FM sample reference tests Annuities. The first ten level payments contribute 147.20. The 19-payment decreasing segment and the final level-1 perpetuity contribute discounted values 72.98 and 3.08. Total is 223.26, choice D.
Independent solution
Setup
Split the stream into ten level payments of 20, a 19-payment sequence 19 down to 1, and a level perpetuity of 1 beginning afterward.
Model
Value the decreasing block at time 10 and the remaining perpetuity at time 29, then discount both to time 0.
Compute
The three present-value components sum to 223.258800.
Answer
The perpetuity value is approximately 223, selecting choice D.
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Original practice · fully worked
A perpetuity pays 30 in each of years 1 through 5. Payments then decline by K each year for ten years; from year 16 onward they remain level at the year-15 amount. At a 5% annual yield, the price is 345.89. Calculate K.
Valuing the first level block, the ten declining payments, and the level tail as functions of K gives a linear price equation. Solving it yields annual decrement 2.00, choice A.
Setup
Separate the five level payments from the ten-step declining block and the permanent level tail.
Model
Set the piecewise present value equal to the quoted market price.
Compute
The resulting linear equation gives K = 2.000000.
Answer
The annual decrement is 2.00, selecting choice A.
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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