Financial mathematics · loans diagnostic PDF
Exam FM Loan Practice Workbook: 30 Fully Worked Problems
Build speed and sign discipline across prospective and retrospective balances, amortization, refinancing, irregular payments, and final-payment adjustments.
One-time USD 19 purchase for a personalized PDF. The 30 original variants are also included in the complete Financial Mathematics Proof Manual; choose this focused diagnostic for curated practice and a lower entry price.
- New practice problems
- 30
- Pages
- 76
- Time limit
- 150 min
- Price
- $19
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One original Exam FM practice question with full solution
A fifteen-year loan at 6% effective has annual payments of 800 for years 1–10 and 600 for years 11–15. Determine the interest portion of payment 11.
- 120.00
- 140.00
- 151.65
- 180.00
- 200.00
Immediately before payment 11 the balance is the value of five 600 payments; 6% of it is 151.65, choice C.
Setup
Immediately after payment ten, only the five smaller payments remain.
Model
Their prospective value is the balance on which year-eleven interest accrues.
Compute
The balance is 2,527.4183, and multiplying by 6% gives 151.6451.
Answer
Thus 151.65 of payment 11 is interest, choice C.
Why the other choices are wrong
- A
- This uses 6% of the 2,000 remaining principal rather than the actual prospective balance.
- B
- This understates the discounted value of the five future payments.
- D
- This treats the balance as 3,000 without discounting future payments.
- E
- This does not equal 6% of the correctly timed outstanding balance.
Independent answer check
| Primary value | 151.645096 |
|---|---|
| Primary method | Value the remaining payments prospectively and apply one period of interest to that balance. |
| Independent value | 151.645096 |
| Independent method | A full amortization schedule separates payment 11 into interest 151.6451 and principal 448.3549. |
| Answer | C · agreement passed |
Contents
Inside the 76-page edition
Candidates preparing in English for the Financial Mathematics (FM) Exam
Table of contents
- 30 original loan and amortization problems
- Prospective and retrospective balance methods
- Principal-interest splits and refinancing
- Final and irregular payment diagnostics
- 120 wrong-choice analyses and two-path checks
What is included
30 verified original variants selected without duplication for this focused diagnostic. 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 focused diagnostic, 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 Loans Practice Workbook
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76 pages · 30 new practice problems · $19