Worked solution · Exam FM
This Exam FM sample reference tests Annuities and Perpetuities. The decreasing payments form a geometric perpetuity with ratio 0.996v; at force 0.06 its value factor is 15.189, so the first payment is 10,000/15.189 = 658.37, choice D.
Independent solution
Setup
The first payment occurs after one year; each later amount is 99.6% of the preceding payment.
Model
Combining payment decline and force-of-interest discounting gives a geometric ratio of 0.996 times exp(−0.06).
Compute
The infinite-series factor is 15.189, and dividing the purchase price by it gives 658.37.
Answer
Thus the first annual payment is approximately 658, choice D.
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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 watershed grant pays 100 at the end of year 1. Every later annual payment is 1% smaller than the preceding payment. Money is discounted at annual force 0.04. Calculate the present value of the grant stream.
The combined payment-and-discount ratio gives present value 1,968.09, choice C.
Setup
Each step from one payment to the next combines a 1% amount reduction with one further year of discounting.
Model
The year-one discounted payment is the first term of a geometric series with ratio 0.99e to the negative 0.04.
Compute
Summing that series gives 1,968.0865.
Answer
The grant stream is worth 1,968.09 today, so choice C is correct.
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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