Worked solution · Exam FM
This Exam FM sample reference tests Annuities and Perpetuities. There are 181 monthly payments from months 60 through 240; discounting the 1% geometric growth against a 0.6% monthly yield gives present value 138,440, choice C.
Independent solution
Setup
The first payment occurs at month 60 and the last at month 240, giving 181 payments.
Model
Factor out the first-payment discount and recognize the remaining terms as a finite geometric series.
Compute
The monthly payment growth exceeds the monthly yield, but the series remains finite and evaluates to about 138,440.
Answer
The annuity present value is 138,440, corresponding to choice C.
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 ten-year annuity pays 500 after one year and grows by g each year. At 6% effective annually its present value is 4,159.40. Determine g.
Solving the ten-payment growing-annuity value equation gives annual growth 3.00%, choice C.
Setup
Place the first 500 payment at year one and let each later payment grow from it.
Model
The discounted payments form a ten-term geometric series in the growth-to-yield ratio.
Compute
Solving the monotone value equation gives growth approximately 0.03.
Answer
The annual payment growth rate is 3.00%, corresponding to 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
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.
