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100+ Free IFoA CM1 Practice Questions

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2026 Statistics

Key Facts: IFoA CM1 Exam

2 papers

Paper A and Paper B

IFoA CM1 guide

70:30

Paper A:B Weighting

IFoA CM1 guide

3h 20m

Paper A Duration

IFoA CM1 guide

1h 50m

Paper B Duration

IFoA CM1 guide

£341

Member Full Fee

IFoA fees page

Core Principles

Qualification Stage

IFoA curriculum

IFoA Subject CM1 (Actuarial Mathematics) is a Core Principles subject on the Associate pathway, assessed by two computer-based papers sat in the same series: Paper A is a 3 hour 20 minute constructed-response paper in Microsoft Word and Paper B is a 1 hour 50 minute applied modelling paper in Microsoft Excel, combined in a 70:30 weighting. The 2026 syllabus spans interest theory and the time value of money, equations of value and loan schedules, project appraisal, survival models and life tables, expected present values of assurance and annuity benefits, reserving, profit testing, and with-profits and unit-linked contracts. IFoA does not publish a fixed question count or percentage pass mark; the examiners set the pass standard each session. Current fees are £341 for members (full rate) and £385 for non-members.

Sample IFoA CM1 Practice Questions

Try these sample questions to test your IFoA CM1 exam readiness. Each question includes a detailed explanation. Start the interactive quiz above for the full 100+ question experience with AI tutoring.

1An investment of £1,000 earns interest at an effective annual rate of 6%. What is the accumulated value after 5 years, to the nearest pound?
A.£1,360
B.£1,500
C.£1,300
D.£1,338
Explanation: Under compound interest the accumulated value is 1000 × (1.06)^5 = 1000 × 1.33823 = £1,338. The accumulation factor (1+i)^n captures interest earned on both principal and previously accumulated interest.
2If the effective annual rate of interest is i = 8%, what is the corresponding effective annual rate of discount d?
A.0.0769
B.0.0864
C.0.0800
D.0.0741
Explanation: The relationship is d = i / (1 + i) = 0.08 / 1.08 = 0.07407, i.e. about 7.41%. Equivalently d = 1 − v where v = 1/(1+i). The discount rate is always less than the interest rate for positive i.
3A nominal annual rate of interest of 12% is convertible monthly. What is the equivalent effective annual rate of interest, to two decimals?
A.12.00%
B.12.36%
C.12.55%
D.12.68%
Explanation: With i^(12) = 0.12, the monthly rate is 0.12/12 = 0.01. The effective annual rate is (1.01)^12 − 1 = 1.12683 − 1 = 0.12683, i.e. 12.68%. Compounding monthly produces a higher effective rate than the nominal rate.
4The force of interest is constant at δ = 0.05 per annum. What is the equivalent effective annual rate of interest i?
A.4.879%
B.5.250%
C.5.000%
D.5.127%
Explanation: The force of interest relates to the effective rate via 1 + i = e^δ. Thus i = e^0.05 − 1 = 1.05127 − 1 = 0.05127, i.e. 5.127%. The force of interest is the continuously compounded rate.
5What is the present value of £5,000 receivable in 8 years' time, valued at an effective annual interest rate of 7%?
A.£2,650
B.£4,673
C.£2,911
D.£3,114
Explanation: Present value = 5000 × v^8 where v = 1/1.07. v^8 = (1.07)^(−8) = 0.58201, so PV = 5000 × 0.58201 = £2,911. Discounting brings a future amount back to its value today.
6The present value of a level annuity-immediate of £1 per annum for n years at rate i is given by which expression?
A.((1 + i)^n − 1) / i
B.(1 − v^n) / δ
C.(1 − v^n) / d
D.(1 − v^n) / i
Explanation: The annuity-immediate present value is a_n = (1 − v^n)/i, with payments at the end of each year. Dividing by d gives the annuity-due value ä_n, and ((1+i)^n − 1)/i is the accumulated value s_n.
7Calculate the present value of a level annuity-immediate paying £1,000 per annum for 10 years at an effective rate of 5%.
A.£10,000
B.£6,139
C.£7,722
D.£8,108
Explanation: PV = 1000 × a_10 = 1000 × (1 − 1.05^(−10))/0.05. Since 1.05^(−10) = 0.61391, a_10 = (1 − 0.61391)/0.05 = 7.7217, so PV = £7,722.
8An annuity-due pays £500 at the start of each year for 6 years. At an effective rate of 4%, the accumulated value of this annuity at the end of year 6 is given by which calculation?
A.500 × s_6
B.500 × ä_6
C.500 × s̈_6
D.500 × a_6
Explanation: Payments made in advance and accumulated to the end of the term use the accumulated annuity-due s̈_6 = ((1+i)^6 − 1)/d. The dots indicate advance payments and the 's' indicates accumulation rather than present value.
9An increasing annuity-immediate pays £1 in year 1, £2 in year 2, ..., £n in year n. Its present value is denoted by which standard actuarial symbol?
A.a_n
B.(I s)_n
C.(Ia)_n
D.(Da)_n
Explanation: The present value of an increasing annuity-immediate with payments 1, 2, ..., n is (Ia)_n = (ä_n − n·v^n)/i. The 'I' denotes increasing payments and the lowercase 'a' denotes a present value of an annuity-immediate.
10A continuously payable annuity pays at a rate of £1 per annum for n years. At force of interest δ, its present value ā_n equals which of the following?
A.(1 − v^n)/d
B.(1 − e^(−n))/δ
C.(1 − v^n)/i
D.(1 − v^n)/δ
Explanation: For a continuously payable annuity, ā_n = ∫₀ⁿ v^t dt = (1 − v^n)/δ, where v^n = e^(−nδ). The denominator is the force of interest δ rather than i or d.

About the IFoA CM1 Exam

IFoA Subject CM1 Actuarial Mathematics covers the theory of interest and the time value of money, equations of value and loan schedules, project appraisal, survival models and life tables, assurance and annuity functions, premiums and reserves, profit testing and the modelling of with-profits and unit-linked contracts.

Assessment

Two computer-based papers in the same series: Paper A constructed-response (Word) and Paper B applied modelling (Excel)

Time Limit

Paper A 3 hours 20 minutes; Paper B 1 hour 50 minutes

Passing Score

Examiner-set pass standard each session; Paper A and Paper B are weighted 70:30 to give the final mark

Exam Fee

£341 member full rate; £385 non-member full rate per series (Institute and Faculty of Actuaries (IFoA))

IFoA CM1 Exam Content Outline

20-25%

Theory of Interest and Time Value of Money

Compound and simple interest, nominal and effective rates, the force of interest, present and accumulated values, annuities-certain, perpetuities, equations of value and allowance for inflation.

15-20%

Equations of Value, Loans and Project Appraisal

Loan schedules and amortisation, prospective and retrospective balances, yields and the internal rate of return, net present value, the discounted payback period and bond pricing.

25-30%

Survival Models and Life Functions

Life tables, the force of mortality, survival and death probabilities, expectation of life, select-and-ultimate mortality, multiple-state Markov models, and assurance and annuity functions including joint-life and last-survivor benefits.

30-35%

Premiums, Reserves and Profit Testing

The equivalence principle, net and gross premiums, prospective and retrospective reserves, death strain at risk, analysis of surplus, profit testing, and the modelling of with-profits and unit-linked contracts.

How to Pass the IFoA CM1 Exam

What You Need to Know

  • Passing score: Examiner-set pass standard each session; Paper A and Paper B are weighted 70:30 to give the final mark
  • Assessment: Two computer-based papers in the same series: Paper A constructed-response (Word) and Paper B applied modelling (Excel)
  • Time limit: Paper A 3 hours 20 minutes; Paper B 1 hour 50 minutes
  • Exam fee: £341 member full rate; £385 non-member full rate per series

Keys to Passing

  • Work through all 100 available questions
  • Review every answer and explanation
  • Track weak areas and revisit them
  • Use our AI tutor for tough concepts

IFoA CM1 Study Tips from Top Performers

1Build fluency with the standard interest and life-contingency symbols so that annuity, assurance, premium and reserve formulae become recall rather than derivation under time pressure.
2Practise loan schedules and project appraisal both prospectively and retrospectively, and learn to find yields by linear interpolation between two trial rates.
3Treat survival models, the force of mortality and select-and-ultimate tables as a connected toolkit rather than isolated formulae, and be ready to value joint-life and last-survivor benefits.
4Master the equivalence principle and reserve recursions, because premiums, prospective and retrospective reserves, death strain at risk and analysis of surplus all build on them.
5Rehearse profit testing and unit-linked projections in Excel exactly as Paper B requires, building transparent, auditable models and sensitivity-testing the key assumptions.

Frequently Asked Questions

How is the IFoA CM1 exam structured?

CM1 is assessed by two computer-based papers sat in the same series. Paper A is a constructed-response paper answered in Microsoft Word and Paper B is an applied modelling paper answered in Microsoft Excel. The two papers are combined in a 70:30 weighting to give the final mark.

How long are the CM1 papers?

Paper A is 3 hours 20 minutes and Paper B is 1 hour 50 minutes. Both papers must be taken within the same examination series, and short additional time is allowed for downloading and uploading exam files.

What is the pass mark for CM1?

IFoA does not publish a fixed percentage pass mark. The examiners set the pass standard for each session, and the final result combines Paper A and Paper B using the 70:30 weighting.

How much does CM1 cost?

For the current series, IFoA lists CM1 at £341 for members at the full rate, with reduced rates for low income, and £385 for non-members at the full rate. Fees are reviewed each year, so check the official IFoA fees page before booking.

What does the CM1 syllabus cover?

CM1 covers the theory of interest and the time value of money, equations of value and loan schedules, project appraisal, survival models and life tables, expected present values of assurance and annuity benefits, premiums and reserves, profit testing, and with-profits and unit-linked contracts.

Where does CM1 fit in the actuarial qualification?

CM1 is one of the Core Principles subjects required on the Associate (ASA) pathway of the IFoA qualification. It builds the actuarial modelling and valuation techniques used throughout later subjects and in life and pensions work.