Worked solution · Exam FM
This Exam FM sample reference tests Annuities. Value the first five payments under 4% growth, then value at time 5 the perpetuity whose next payment reflects the fifth 4% increase and grows 8% thereafter. The two components are 3.87 and 17.26, totaling 21.13; choice A.
Independent solution
Setup
Separate the first five payments from the later perpetuity because the growth rate changes after the fifth 4% increase.
Model
At time 5, the tail begins with payment 1.04 to the fifth and then grows at 8%.
Compute
The finite block is 3.870481 and the tail is 17.259038, giving total 21.129519.
Answer
The perpetuity present value is approximately 21.13, selecting choice A.
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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 perpetuity pays 1 at year 1. Payments initially grow 3% annually; after N early payments, all later payments grow 6% annually. At a 10% yield, the price is 22.5222. Determine N.
Testing the finite early-growth block together with the later 6%-growth tail shows the quoted price is produced by N = 4 early payments, choice B.
Setup
For a candidate N, value the first N payments under 3% growth.
Model
At time N, append the perpetuity tail beginning with the next 3%-grown payment and then growing 6%.
Compute
The sum matches the quoted price at N = 4.
Answer
There are 4 early-growth payments, selecting choice B.
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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