Worked solution · Exam FM
This Exam FM sample reference tests Linking a Force of Interest to Nominal Discount. The force simplifies to 1/(10+t), so 1000 grows from time 2 to 6 by 16/12, giving X = 1333.33. Discounting this back eight quarters at 2% discount per quarter gives Y = 1134.35, choice C.
Independent solution
Setup
Simplify the stated force and integrate over the investment interval.
Model
The continuous-force accumulation is a ratio of endpoints.
Compute
A nominal discount rate of 8% convertible quarterly has quarterly discount 2%.
Answer
The required initial amount is approximately 1134, 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 1,000 deposit grows from time 0 to time 4 under force of interest 1/(4+t). A separate 1,500 deposit must reach the same terminal amount in two years under a nominal annual discount rate d convertible semiannually. Determine d.
The force path doubles 1000 to 2000. Solving 1500 accumulated through four semiannual discount periods to 2000 gives d = 13.8790%, choice C.
Setup
Integrate the force to find the common terminal target.
Model
A semiannual nominal discount rate uses discount d divided by two each half-year.
Compute
Solve the fourth-power equation.
Answer
The nominal discount rate is 13.88%, choice C.
Keep practicing
These references share syllabus concepts or sit nearby in the official sequence. All 51 Exam FM time value of money 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.
