Worked solution · Exam FM
This Exam FM sample reference tests Annuities and Perpetuities. The effective monthly rate is 0.52617%; accumulating the level 1,097 component and the five-per-month increasing component for 180 months gives 442,031, choice A.
Independent solution
Setup
Only the first 180 monthly payments are accumulated, and the first of those is 1,102.
Model
Rewrite payment k as a level 1,097 plus an increasing component 5k.
Compute
At the monthly rate equivalent to 6.5%, the two accumulated components total 442,031.
Answer
The accumulated value after 15 years is 442,031, which is choice A.
Test the method on unseen problems
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 community garden contributes 200 at the end of year 1, then raises each annual contribution by 20 through year 15. At 7% effective annually, calculate the fund immediately after the year-15 contribution.
Accumulating the 15 arithmetic payments to year 15 gives 7,919.81, choice C.
Setup
Contribution k equals 200 plus 20 times k minus one and accumulates for 15 minus k years.
Model
Separate the level 200 stream from the arithmetic step component.
Compute
Evaluating both accumulated annuity parts at 7% gives 7,919.8107.
Answer
The year-15 fund is 7,919.81, which is 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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