Worked solution · Exam FM
This Exam FM sample reference tests Arithmetic-Increasing Perpetuity-Due. The two receipts are worth 1821927.11 today. An arithmetic perpetuity-due has value X times 26 plus the 1000 increments' value 650000. Solving gives X = 45074.12, choice A.
Independent solution
Setup
Value the two original receipts at time zero.
Model
A level perpetuity-due of X has factor one plus i divided by i. The 1000 arithmetic increments use the increasing-perpetuity factor.
Compute
Equate values and isolate the first payment.
Answer
The first payment is approximately 45074, choice A.
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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.
Error diagnosis
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Original practice · fully worked
Five annual payments occur at times 0 through 4. The first is 2,000 and each later payment is 100 larger. At a 5% yield, replace them by five equal payments on the same dates. Determine the level payment.
The arithmetic stream has present value 9956.78. Dividing by the five-payment annuity-due factor gives a level payment of 2190.25, choice C.
Setup
Discount the five arithmetic payments at their actual dates.
Model
Let L be the equal payment on dates zero through four.
Compute
Divide by the due-annuity factor.
Answer
The equivalent level payment is 2190.25, choice C.
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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.
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