Worked solution · Exam FM
This Exam FM sample reference tests Interest Rate Measures. Writing the present-value equality as a quadratic in v produces discount factors 0.970874 and 0.952381, corresponding to 3% and 5% annual rates. Their absolute difference is 2%, so choice B is correct.
Independent solution
Setup
Let v be the one-year discount factor and write the common present-value equation.
Model
Solve the quadratic for its two positive discount-factor roots.
Compute
Converting by i = 1/v − 1 gives rates 3.00% and 5.00%, whose difference is 2.00%.
Answer
The rates differ by 2.0%, 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
The present value of 8,550 now plus 10,000 at year 2 equals the present value of 18,500 at year 1 at two positive annual effective rates. Calculate the sum of those two rates.
The value equation factors into discount roots 0.95 and 0.90. These correspond to rates 5.26% and 11.11%, whose sum is 16.37%, choice B.
Setup
Write the equality as a quadratic in the annual discount factor.
Model
Factor the quadratic to obtain both positive discount roots.
Compute
The corresponding rates are 5.263158% and 11.111111%, summing to 16.374269%.
Answer
The sum of the two rates is 16.37%, selecting choice B.
Keep practicing
These references share syllabus concepts or sit nearby in the official sequence. All 51 Exam FM time value of money practice problems.
Drill the method: Exam FM Annual Force of Interest and Rate Conversion problems
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