Financial mathematics · 150-minute practice PDF
Exam FM Practice Exam I: 30 Questions with Full Solutions
Rehearse the complete current Financial Mathematics syllabus in one 30-question sitting, then diagnose every model choice with full solutions and four specific wrong-choice analyses.
One-time USD 39 purchase for a personalized PDF. The 30 original variants are also included in the complete Financial Mathematics Proof Manual; choose this full-length timed form for curated practice and a lower entry price.
- New practice problems
- 30
- Pages
- 76
- Time limit
- 150 min
- Price
- $39
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One original Exam FM practice question with full solution
A perpetuity pays 1, 2, 3, 4, and 5 at the ends of years 1 through 5, then pays 5 every year thereafter. At 10% annual interest, find its present value.
- 38.25
- 40.00
- 41.70
- 43.55
- 45.00
The finite staircase plus deferred perpetuity totals 41.69865, or 41.70. This selects choice C.
Setup
Discount the five increasing payments explicitly, then value the level perpetuity that begins after payment 5.
Model
The perpetuity is worth 5/0.10 at time 5; multiplying by v⁵ moves it to time 0.
Compute
The finite staircase plus deferred perpetuity totals 41.69865, or 41.70.
Answer
The requested value is 41.70, so the correct choice is C.
Why the other choices are wrong
- A
- Choice A (38.25) does not match the checked five-step payment staircase result (41.70); no distinct standard one-step error is identifiable.
- B
- Choice B (40.00) does not match the checked five-step payment staircase result (41.70); no distinct standard one-step error is identifiable.
- D
- Choice D (43.55) does not match the checked five-step payment staircase result (41.70); no distinct standard one-step error is identifiable.
- E
- Choice E (45.00) does not match the checked five-step payment staircase result (41.70); no distinct standard one-step error is identifiable.
Independent answer check
| Primary value | 41.698654 |
|---|---|
| Primary method | Evaluate the authored cash-flow equation using increasing perpetuity. |
| Independent value | 41.698654 |
| Independent method | Five deferred unit perpetuities give the same value. |
| Answer | C · agreement passed |
Contents
Inside the 76-page edition
Candidates preparing in English for the Financial Mathematics (FM) Exam
Table of contents
- 150-minute candidate plan and printable answer sheet
- 30 syllabus-balanced five-choice questions
- Answer key and complete worked solutions
- 120 concrete wrong-choice analyses
- Two-path verification for every answer
What is included
30 verified original variants selected without duplication for this full-length timed form. Official problem wording is not included.
Verification
Every included result is reproducible
Every selected problem already passed a reproducible calculation, an independent second method, and answer-letter agreement. The compiler rejects any failed check, cross-product duplicate, or official source wording.
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Questions about this edition
Are these official sample questions?
No. Every question is an independently written original variant. Official problem wording is not reproduced.
Are complete solutions included?
Yes. Every problem includes Setup, Model, Compute, and Answer steps plus a concrete explanation for each of the four incorrect choices.
How are the answers checked?
Each answer must agree under a reproducible primary calculation and a distinct independent method before the PDF can build.
Does this overlap the complete proof manual?
Yes. These 30 original variants are selected from the verified variant bank included in the Financial Mathematics Proof Manual. This edition adds a curated full-length timed form, answer sheet, answer key, and focused purchase price.
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ActuaryProof is not affiliated with, endorsed by, or sponsored by the Society of Actuaries. Exam names are used solely to identify the exams for which these study materials are relevant. All problems and solutions are original works.
Financial Mathematics Practice Examination I
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