Worked solution · Exam FM
This Exam FM sample reference tests Annuities and Perpetuities. The first five due payments are worth 94,341.97; discounting the later 50,000 perpetuity back through the first rate regime leaves an equation whose solution is i = 5%, choice C.
Independent solution
Setup
Value the first five beginning-of-year payments under the initial 3% rate.
Model
At time five, the continuing payments form a perpetuity-due under the later rate.
Compute
Move the remaining value to time five and solve the due-perpetuity equation.
Answer
The later annual effective rate is 5.00%, corresponding to choice C.
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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 perpetuity-due pays 15,000 for its first four payments and 40,000 thereafter. The first four years use 4% effective interest and later valuation uses 6%. Determine the present value.
The four temporary payments plus the time-four value of the continuing due perpetuity total 660,688, choice C.
Setup
Value the first four beginning-of-year payments at the initial rate.
Model
At time four, value the continuing level stream as a perpetuity-due at 6%.
Compute
Discount that continuation through the first four-year regime and add both components.
Answer
The present value is approximately 660,688, corresponding to 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.
Drill the method: Exam FM Annuities and Perpetuities problems
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