Worked solution · Exam FM
This Exam FM sample reference tests Annuities and Perpetuities. Decomposing the increasing payments into deferred level perpetuities gives present value vⁿ/i², equivalently vⁿ/d², which is choice D.
Independent solution
Setup
View the payment of k units as k overlapping unit perpetuities beginning at successive dates.
Model
The values of those deferred level perpetuities themselves form a geometric series.
Compute
Summing that series and using d = iv converts the result to v to the n divided by d squared.
Answer
That symbolic form appears in choice D.
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Error diagnosis
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Original practice · fully worked
A public-art trust pays 2 at the end of year 3, 4 at the end of year 4, 6 at the end of year 5, and continues increasing by 2 forever. At 5% effective annually, calculate the present value at time zero.
A two-year deferral applied to twice an increasing perpetuity gives 761.90, choice C.
Setup
Removing the two-year deferral leaves payments 2, 4, 6, and so on at consecutive year-ends.
Model
That stream is twice the standard increasing perpetuity-immediate and must then be discounted two years.
Compute
The increasing-perpetuity factor is 1.05 divided by 0.05 squared; applying the deferral gives 761.9048.
Answer
The trust's present value is 761.90, 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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