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100+ Free IAI CM1 Practice Questions

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Key Facts: IAI CM1 Exam

CM1

Core Principles Subject

IAI syllabus

2 papers

Written plus Computer-based

IAI exam format

~5 hrs

Combined Exam Time

IAI exam format

~250 hrs

Recommended Study

CM1 curriculum

100

Practice Questions

OpenExamPrep

India

Jurisdiction

Institute of Actuaries of India

IAI Subject CM1 Actuarial Mathematics is a Core Principles exam assessed by a paper-based written paper of about 3 hours 15 minutes plus a computer-based (Excel) paper of about 1 hour 45 minutes, both sat in the same diet and combined for a single mark. The IAI syllabus mirrors the IFoA CM1 curriculum for the India jurisdiction, covering the theory of interest, the equation of value, survival models and life tables, assurances and annuities, premiums and reserves, and profit testing. IAI sets the pass mark each diet and does not publish a fixed percentage; the recommended study load is around 250 hours.

Sample IAI CM1 Practice Questions

Try these sample questions to test your IAI 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 ₹10,000 grows to ₹12,100 after 2 years under annual compound interest. What is the effective annual rate of interest?
A.10%
B.10.5%
C.21%
D.5%
Explanation: Under compound interest, 10000(1+i)^2 = 12100, so (1+i)^2 = 1.21 and 1+i = 1.1, giving i = 10%. The accumulation factor is (1+i)^t for compound interest.
2If the nominal rate of interest convertible quarterly is 8% per annum, what is the equivalent effective annual rate of interest?
A.8.00%
B.8.24%
C.8.16%
D.2.00%
Explanation: With i^(4) = 0.08, the quarterly rate is 0.02. The effective annual rate is (1 + i^(4)/4)^4 - 1 = 1.02^4 - 1 = 0.0824, i.e. 8.24%. Nominal rates must be converted via the compounding frequency.
3The force of interest is constant at δ = 0.06 per annum. What is the present value of ₹1 payable in 5 years?
A.0.7000
B.0.7835
C.0.7408
D.0.9418
Explanation: Under a constant force of interest, the discount factor is v^t = e^(-δt) = e^(-0.06×5) = e^(-0.3) ≈ 0.7408. The force of interest links to the discount factor through continuous compounding.
4Which relationship correctly links the annual effective rate of interest i, the rate of discount d, and the discount factor v?
A.d = i + v
B.d = i / (1 + i)^2
C.d = 1 + i
D.d = i × v
Explanation: Since v = 1/(1+i) and d = i/(1+i), we have d = i × v. Equivalently d = 1 - v. These identities relate the equivalent measures of interest and discount.
5An accumulation function is given by A(t) = 1 + 0.04t + 0.002t^2. What is the force of interest δ(t) at time t = 5?
A.0.0480
B.0.0600
C.0.0400
D.0.0500
Explanation: δ(t) = A'(t)/A(t). Here A'(t) = 0.04 + 0.004t, so A'(5) = 0.06 and A(5) = 1 + 0.2 + 0.05 = 1.25. Thus δ(5) = 0.06/1.25 = 0.048. The force of interest is the logarithmic derivative of the accumulation function.
6What is the accumulated value at the end of 10 years of ₹1 invested now, if the force of interest is δ = 0.05 per annum throughout?
A.1.6289
B.1.6487
C.1.5000
D.1.6105
Explanation: Under constant force, the accumulation factor is e^(δt) = e^(0.05×10) = e^(0.5) ≈ 1.6487. The force of interest accumulates continuously.
7The present value of an annuity-immediate paying ₹1 per year for n years at rate i is given by which formula?
A.(1 - v^n)/d
B.(v^n - 1)/i
C.(1 - v^n)/i
D.(1 - v^n) × i
Explanation: The present value of a level annuity-immediate is a_n = (1 - v^n)/i, summing v + v^2 + ... + v^n. Payments are made at the end of each period.
8At i = 5% per annum, what is the present value of an annuity-due paying ₹1,000 at the start of each year for 4 years?
A.₹3,546
B.₹3,902
C.₹4,000
D.₹3,723
Explanation: ä_4 = (1 - v^4)/d where v^4 = 1.05^-4 = 0.8227 and d = 0.05/1.05 = 0.04762. So ä_4 = (1 - 0.8227)/0.04762 = 3.7232, giving ₹3,723. Annuity-due payments are at period start.
9The accumulated value of an annuity-immediate of ₹1 per year for n years at rate i is denoted s_n. Which expression is correct?
A.((1+i)^n - 1)/i
B.(1 - (1+i)^n)/i
C.((1+i)^n - 1)/d
D.(1 - v^n)/i
Explanation: s_n = ((1+i)^n - 1)/i is the future value at time n of payments of 1 at the end of each year. It equals a_n × (1+i)^n.
10An increasing annuity-immediate pays ₹1 at the end of year 1, ₹2 at the end of year 2, and so on up to ₹n. Its present value (Ia)_n equals:
A.(a_n - n·v^n)/i
B.(ä_n - n·v^n)/i
C.n·v^n/i
D.ä_n × n
Explanation: The present value of an increasing annuity-immediate is (Ia)_n = (ä_n - n·v^n)/i, where ä_n is the annuity-due factor. The increasing payment structure builds on the standard annuity.

About the IAI CM1 Exam

IAI Subject CM1 Actuarial Mathematics is a Core Principles actuarial exam that tests the theory of interest, equation of value, survival models, life-table functions, assurances and annuities, premium and reserve calculation, and profit testing in the India jurisdiction.

Assessment

Written constructed-response paper plus a computer-based modelling paper, both sat in the same diet and combined for one result

Time Limit

About 3 hours 15 minutes written plus about 1 hour 45 minutes computer-based

Passing Score

Pass mark set by IAI each diet; IAI does not publish a fixed percentage

Exam Fee

Varies by IAI member category; see the official IAI exam-fees page (Institute of Actuaries of India (IAI))

IAI CM1 Exam Content Outline

Core

Theory of Interest and Financial Mathematics

Compound interest, nominal and effective rates, the force of interest, discounting, level and increasing annuities, perpetuities, real versus money rates, and the term structure of interest rates including spot and forward rates.

Core

Equation of Value and Applications

Setting up and solving equations of value for loan repayment schedules, bond pricing and yields, project appraisal, net present value, internal rate of return, and discounted payback periods.

Core

Survival Models and Life-Table Functions

Force of mortality, survival probabilities, life-table functions, Gompertz and Makeham laws, fractional-age assumptions, select and ultimate mortality, joint-life and last-survivor statuses, and multiple-state and multiple-decrement models.

Core

Assurances, Annuities, Premiums, Reserves and Profit Testing

Expected present values of assurance and annuity contracts, commutation functions, net and gross premiums, the equivalence principle, prospective and retrospective policy values, Thiele's equation, death strain at risk, mortality profit, and profit-testing cashflow projections.

How to Pass the IAI CM1 Exam

What You Need to Know

  • Passing score: Pass mark set by IAI each diet; IAI does not publish a fixed percentage
  • Assessment: Written constructed-response paper plus a computer-based modelling paper, both sat in the same diet and combined for one result
  • Time limit: About 3 hours 15 minutes written plus about 1 hour 45 minutes computer-based
  • Exam fee: Varies by IAI member category; see the official IAI exam-fees page

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

IAI CM1 Study Tips from Top Performers

1Build instant recall of the interest functions: effective and nominal rates, the force of interest, discount factors, and annuity and perpetuity formulae become setup work rather than derivations under time pressure.
2Practice the equation of value across loan schedules, bond pricing, and project appraisal so you can switch quickly between NPV, IRR, and payback questions.
3Drill life-table functions and survival probabilities until you can move confidently between l_x, q_x, p_x, the force of mortality, and select-and-ultimate notation.
4Treat premiums and reserves as one workflow: apply the equivalence principle, then compute prospective and retrospective policy values and recursive reserves consistently.
5Rehearse profit-testing cashflow projections, including the profit vector, profit signature, risk discount rate, and profit margin, because the computer-based paper rewards a clean, repeatable Excel method.

Frequently Asked Questions

What is IAI Subject CM1?

CM1 Actuarial Mathematics is a Core Principles exam of the Institute of Actuaries of India. It covers the theory of interest, the equation of value, survival models, life contingencies, premiums, reserves, and profit testing, mirroring the IFoA CM1 curriculum for the India jurisdiction.

How is the IAI CM1 exam structured?

CM1 is assessed by a paper-based written constructed-response paper of about 3 hours 15 minutes plus a computer-based (Excel) modelling paper of about 1 hour 45 minutes. Both papers are sat in the same diet and combined for a single mark; there is no fixed multiple-choice question count.

What is the passing score for IAI CM1?

IAI sets the pass mark for each exam diet and does not publish a fixed percentage. Both the written and computer-based components count toward one combined result.

Which topics does IAI CM1 cover?

The syllabus covers the theory of interest and financial mathematics, the equation of value, survival models and life-table functions, assurances and annuities, premium and reserve calculation, and profit testing. CM1 emphasises application, with a smaller share of knowledge and higher-order skills.

How much study time does IAI CM1 need?

The recommended study load is around 250 hours, which most candidates spread over four to six months. Strong fluency in interest theory and life-contingencies formulae is essential because both papers are calculation-heavy.

Does IAI CM1 mirror the IFoA CM1 exam?

Yes. The IAI CM1 syllabus follows the IFoA Actuarial Mathematics for Modelling (CM1) Core Principles curriculum, adapted to the India jurisdiction, so candidates study the same deterministic-modelling and life-contingencies material.