Worked solution · Exam FM
This Exam FM sample reference tests Annuities and Perpetuities. The two quoted annuity values are n−1 half-years apart; combining their ratio with the annuity-due value equation gives half-year rate 8.5%, equivalent to 17.72% annually, choice E.
Independent solution
Setup
The first-payment and last-payment value dates are separated by n minus one half-year periods.
Model
Use their ratio to replace the terminal discount factor inside the annuity-due present-value expression.
Compute
That substitution isolates the half-year rate at 8.5%.
Answer
Compounding twice gives annual effective rate 17.72%, which rounds to choice E.
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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 level quarterly annuity has value 5,000 at the time of its first payment and accumulated value 7,000 at the time of its twelfth and final payment. Determine the equivalent annual effective interest rate.
The two value dates are 11 quarters apart; their ratio gives 3.106% quarterly and 13.02% annually, choice C.
Setup
The first and twelfth payment dates are separated by eleven quarterly accumulation periods.
Model
Their value ratio directly determines the quarterly accumulation factor without needing the payment amount.
Compute
The quarterly rate is 3.10610%; compounding it over four quarters gives 13.01536%.
Answer
The annual effective rate is 13.02%, corresponding to choice C.
Calculator reproduction
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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
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