Worked solution · Exam FM
This Exam FM sample reference tests Annuities and Perpetuities. One year's quarterly pattern has value 100 times the four-period increasing-annuity factor at 3%; annual repetition begins immediately and uses annual effective rate 12.551%, giving the equation in choice E.
Independent solution
Setup
First value the four quarterly payments within a representative year at that year's beginning.
Model
The amounts 100 through 400 form an increasing annuity-immediate over four quarters.
Compute
Those yearly blocks repeat at times zero through nine, so their block values form an annual annuity-due.
Answer
Using the equivalent annual rate 12.55% gives the equation in choice E.
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Error diagnosis
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Original practice · fully worked
For three years, a fund pays 50, 100, 150, and 200 at the ends of the four quarters in each year. Interest is 8% nominal convertible quarterly. Determine the present value.
Value one quarterly pattern and then three beginning-of-year block values; the result is 1,308.83, choice C.
Setup
Value the four increasing quarter-end payments at the start of one year.
Model
Convert the quarterly rate to the effective annual rate for repeating blocks.
Compute
The three block values occur at years zero, one, and two, forming an annuity-due.
Answer
The present value is 1,308.83, 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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