Worked solution · Exam FM
This Exam FM sample reference tests Annuities and Perpetuities. The nine-unit annual increases have present value 2,500, leaving 100 of value for the level P perpetuity; therefore P/0.06 = 100 and P = 6, choice B.
Independent solution
Setup
Decompose the payments into a level perpetuity of P and an arithmetic increase of nine per year.
Model
The increasing component's discounted value is 2,500 under the stated timing and rate.
Compute
Only 100 of the total price remains for the level perpetuity, so its annual payment is 100 times 0.06.
Answer
The first payment is 6.00, corresponding to choice B.
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Original practice · fully worked
A civic stipend pays P after one year and then increases by 5 each year forever. At 8% effective annually, the stream is worth 1,800. Determine P.
Removing the five-unit arithmetic increase value leaves a level perpetuity with P = 81.50, choice C.
Setup
Write the annual payment as a level P plus an increment of five times year index minus one.
Model
The delayed arithmetic increments have present value five divided by i squared.
Compute
After removing 781.25 from the total value, the level perpetuity component is 1,018.75.
Answer
Multiplying by 8% gives first payment 81.50, choice C.
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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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