Worked solution · Exam FM
This Exam FM sample reference tests Annuities. The ten payments form a finite geometric stream with payment growth 15% and discount rate 5%. Direct valuation gives 1483.62, so choice E is correct.
Independent solution
Setup
Payment k is the first payment grown by 15% for k minus 1 years.
Model
Discount the ten-term geometric stream at 5%.
Compute
Evaluating the finite geometric sum gives 1483.621512.
Answer
The annuity present value is approximately 1,484, so choice E is correct.
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 six-payment annuity pays 500 at year 1, and each later payment grows by the same annual rate g. At a 4% annual yield, its present value is 2816.16. Calculate g.
Equating the six-term geometric payment stream to the quoted price and solving for its common growth rate gives 3.00%, choice D.
Setup
Write all six payments from the unknown common growth rate.
Model
Set their discounted value at 4% equal to the quoted price.
Compute
The economically relevant root is g = 3.0000%.
Answer
The annual payment growth rate is 3.00%, selecting choice D.
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
Keep studying
Work through the related free solutions for this topic, review the formulas you used, or keep every current Exam FM solution in one searchable PDF.
