Worked solution · Exam FM
This Exam FM sample reference tests Annuities. There are 18 withdrawals from ages 65 through 82 inclusive. Accumulating the original fund for 17 years and subtracting the accumulated withdrawals while restoring the 1,000,000 ending fund gives P = 88915.43, choice B.
Independent solution
Setup
Use the 82nd birthday immediately after withdrawal as the comparison date; 17 years have elapsed since age 65.
Model
The withdrawals at times 0 through 17 accumulate as an 18-payment annuity-immediate shifted to the terminal date.
Compute
Solving the terminal balance gives withdrawal 88915.4343.
Answer
The annual birthday withdrawal is approximately 88,915, selecting choice B.
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 reserve contains 500,000 immediately before an initial withdrawal of 40,000. It earns 6% annually, and another 40,000 is withdrawn after each of the next ten years. Calculate the balance immediately after the tenth-year withdrawal.
The original reserve accumulates ten years, while the eleven withdrawals from time 0 through time 10 accumulate as an eleven-term series. The resulting balance is 296,558.14, choice D.
Setup
Use the date immediately after the time-10 withdrawal as the comparison date.
Model
Recognize the withdrawal accumulation as an eleven-payment accumulated annuity.
Compute
The resulting ending reserve is 296558.14.
Answer
The balance after the final withdrawal is 296,558.14, 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.
