Worked solution · Exam FM
This Exam FM sample reference tests Accumulation Followed by a Perpetuity. Equating the 45-deposit accumulation to the perpetuity price makes the 45-year accumulation factor equal to 10. Thus i = 5.2500% and the fund is 1199.99, choice C.
Independent solution
Setup
The deposits accumulate to seven times s-angle-45 at rate i. The same fund buys a perpetuity-immediate at rate 1.2i.
Model
Equate the two expressions and cancel i.
Compute
The equation gives an accumulation of ten over 45 years.
Answer
The accumulated fund rounds to 1200, 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.
Error diagnosis
These notes identify the calculation error associated with each wrong letter when that error is reproducible.
Original practice · fully worked
A saver deposits 10 at each year-end into an account earning 4% effective. Immediately after the last deposit, the balance buys a perpetuity-immediate priced at 5% and paying 14.8890 annually. How many deposits were made?
The perpetuity costs 297.7800. Solving 10s-angle-n at 4% equal to that amount gives n = 20, choice C.
Setup
Translate the perpetuity payment into the fund required at purchase.
Model
The year-end deposits accumulate as an annuity-immediate.
Compute
Isolate the accumulation factor and solve its exponent.
Answer
The saver made 20 deposits, 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.
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.
