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Study notes
Clear, concise notes for each subject, organised by syllabus topic, with formulas, examples and exam tips. Download as PDF.
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Full-length papers that match the real exam's format, timing and topic weighting, each with a complete memo. Download as PDF.
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Built for candidates who want more practice than the official sample questions provide.
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Always on syllabus
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Detailed worked solutions
Every question explains the method, not just the answer, including the common traps behind wrong options.
Sample questions
Four questions from our question bank. Try them, then open the worked solution.
Payments of 500 are made at the end of each year for 10 years into a fund earning an annual effective interest rate of 5%. Calculate the accumulated value of the fund immediately after the last payment.
- (A) 5,000.00
- (B) 6,144.47
- (C) 6,288.95
- (D) 6,603.39
- (E) 8,144.47
Show worked solution
The accumulated value of an annuity-immediate is 500 · s10| at 5%.
s10| = (1.0510 − 1) / 0.05 = (1.628895 − 1) / 0.05 = 12.577893
500 × 12.577893 = 6,288.95
Answer: (C). Option (D) is the annuity-due value (payments at the start of each year).
A bank quotes a nominal annual interest rate of 6% compounded monthly. Calculate the equivalent annual effective interest rate.
- (A) 6.000%
- (B) 6.090%
- (C) 6.136%
- (D) 6.168%
- (E) 6.184%
Show worked solution
The monthly effective rate is 0.06 / 12 = 0.005.
i = (1.005)12 − 1 = 1.061678 − 1 = 0.061678
Answer: (D) 6.168%. Options (B) and (C) come from semi-annual and quarterly compounding; option (E) from continuous compounding.
A loan of 20,000 is repaid with level monthly payments at the end of each month for 5 years. The nominal annual interest rate is 9% compounded monthly. Calculate the monthly payment.
- (A) 333.33
- (B) 398.32
- (C) 415.17
- (D) 418.28
- (E) 483.33
Show worked solution
The monthly rate is j = 0.09 / 12 = 0.0075, with n = 60 payments.
a60| = (1 − 1.0075−60) / 0.0075 = (1 − 0.638700) / 0.0075 = 48.173374
P = 20,000 / 48.173374 = 415.17
Answer: (C). Option (A) ignores interest entirely; option (E) adds simple interest to the principal.
For events A and B: P(A) = 0.6, P(B) = 0.5 and P(A ∪ B) = 0.8. Calculate P(A | B).
- (A) 0.30
- (B) 0.50
- (C) 0.60
- (D) 0.75
- (E) 0.80
Show worked solution
By inclusion–exclusion: P(A ∩ B) = 0.6 + 0.5 − 0.8 = 0.3
P(A | B) = P(A ∩ B) / P(B) = 0.3 / 0.5 = 0.6
Answer: (C). Since P(A | B) = P(A), the events are independent.
Exams
We launch with two exams and add more based on demand. Each exam has study notes, quizzes and practice papers.
| Exam | Body | Status |
|---|---|---|
| Exam P — Probability | SOA | Launching first |
| Exam FM — Financial Mathematics | SOA | Launching first |
| CM1 / CS1 | IFoA | Planned |
| A211 Financial Mathematics | ASSA | Planned |
Want a specific exam added? Tell us which one.
Questions
The short answers.
Are these real past exam questions?
No. Every question and every page of notes is original, written to the published syllabus and learning objectives. We never reproduce past papers or copyrighted study material.
What is the difference between quizzes and practice papers?
Quizzes are short, online and focused on one topic at a time, with instant marking. Practice papers are full-length mock exams in PDF, matching the real exam's format and timing, with a complete memo.
How do you know the answers are right?
Numerical answers are calculated by code, separately from the written solution, and every step in the solution is checked against that calculation. Each question also has a report button so errors are fixed fast.
Do I need the study notes if I have an official study manual?
Not necessarily. Our notes are a concise companion for learning and revision. Many candidates use them alongside their main study material.
When does it launch?
Soon, starting with SOA Exam P and Exam FM. Email hello@mintedpapers.com with any questions.
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