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100+ Free IAI CM1 Practice Questions

IAI Subject CM1 Actuarial Mathematics practice questions are available now; exam metadata is being verified.

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The term structure of interest rates is best described by which of the following relationships?

A
B
C
D
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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 Practice Questions

Verified exam format metadata for IAI Subject CM1 Actuarial Mathematics is pending. The practice questions above remain available while official exam length, timing, passing score, fee, and administrator details are reviewed.