CM1 — Actuarial Mathematics

CM1 introduces the time value of money and the mathematics of contingent cash flows — the two ideas at the heart of actuarial work. You’ll learn to construct equations of value, build loan and reserve schedules, evaluate investment projects, and apply survival models to price and reserve for life assurance and annuity contracts.

Under the pre-2019 exam structure, this single subject combined two separate papers: CT1 (Financial Mathematics) and CT5 (Contingencies). That split still maps neatly onto CM1’s two halves — the first eleven chapters build the financial mathematics toolkit (old CT1 territory), and the remaining fourteen apply it to mortality and life insurance contracts (old CT5 territory). Thinking of CM1 this way helps make sense of why the subject suddenly shifts gears around the halfway point.

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Chapter List — CT1 vs CT5

CT1 (Financial Mathematics)

  • 1. The time value of money
  • 2. Interest rates
  • 3. Real and money interest rates
  • 4. Discounting and accumulating
  • 5. Level annuities
  • 6. Increasing annuities
  • 7. Equations of value
  • 8. Loan schedules
  • 9. Project appraisal
  • 10. Bonds, equity and property
  • 11. Term structure of interest rates

CT5 (Contingencies)

  • 12. The life table
  • 13. Life assurance contracts
  • 14. Life annuity contracts
  • 15. Evaluation of expenses and annuities
  • 16. Variable benefits and conventional with-profits policies
  • 17. Gross premiums
  • 18. Gross premium reserves
  • 19. Joint life and last survivor benefits
  • 20. Contingent and reversionary benefits
  • 21. Mortality profit
  • 22. Competing risks
  • 23. Unit-linked and conventional with-profits contracts
  • 23. Profit testing
  • 23. Reserving aspects of profit testing

PART 1 : — Financial Mathematics (maps to old CT1) — Chapters 1–11

Group A :— Foundations of Interest (Chapters 1–4: The time value of money, Interest rates, Realand money interest rates, Discounting and accumulating)

This is where every actuarial calculation ultimately starts: money today is worth more than the same money tomorrow, and you need a rigorous way to compare cash flows that happen at different points in time. Students learn how to move money forwards (accumulate) and backwards (discount) in time using simple and compound interest, how nominal and effective interest rates relate to each other, and the crucial distinction between “real” interest rates (adjusted for inflation) and “money” (nominal) interest rates. In practice, this is the same logic a bank uses to quote you a loan rate, a pension fund uses to work out what a rupee promised in 2050 is worth today, or an investor uses to compare a fixed deposit against an inflation-linked bond.

Group B : — Annuities and Loans (Chapters 5–8: Level annuities, Increasing annuities, Equations of value, Loan schedules)

Very few real cash flows are single lump sums — most are streams of payments, like EMIs, rent, or salary. This block teaches you to value annuities (level and increasing), and introduces the “equation of value,” the single most-used tool in the entire actuarial toolkit — it’s simply the idea that at a fair price, the present value of what you pay equals the present value of what you receive. From there, loan schedules show you how to break a loan repayment into interest and capital components period by period — exactly what a bank does when it generates your home loan amortisation table.

Group C : — Investment Appraisal (Chapters 9–11: Project appraisal, Bonds, equity and property, Term structure of interest rates)

This group moves from valuing simple cash flows to making investment decisions. Project appraisal introduces metrics like Net Present Value (NPV) and Internal Rate of Return (IRR) — the same tools used by corporate finance teams to decide whether a factory expansion or a new product line is worth funding. The bonds, equity and property chapter applies the equation of value to real asset classes, showing students how to price a bond given its coupon and redemption terms, or estimate a fair value for equity and property investments. Term structure of interest rates then explains why a 1-year loan and a 10-year loan don’t carry the same interest rate — essential for anyone pricing long-duration insurance liabilities.

PART 2 : — Contingencies (maps to old CT5) — Chapters 12–25

Group D : — Mortality Foundations (Chapter 12: The life table)

The pivot point of the subject. Life tables are the actuarial equivalent of a weather forecast for human survival — a structured way of recording the probability that someone of a given age survives to older ages, or dies within the next year. Every later chapter in CM1 (and, honestly, most of the actuarial career that follows) depends on being fluent in life table notation and the probabilities built from it.

Group E : — Life Insurance Contracts (Chapters 13–16: Life assurance contracts, Life annuity contracts, Evaluation of expenses and annuities, Variable benefits and conventional with-profits policies)

Here, students combine the time-value-of-money skills from Part 1 with the mortality skills from Chapter 12 to price real insurance products. Life assurance contracts (like term insurance or whole life policies) pay out on death; life annuity contracts pay out for as long as someone survives — pension products are a direct real-world example. The expenses chapter adds a dose of realism: insurers have to load their pricing for commission, administration, and claimshandling costs, not just the “pure” mortality risk. Variable benefits and with-profits policies then introduce products where the payout isn’t fixed in advance but depends on the insurer’s investment performance — the kind of policy still widely sold in the Indian life insurance market today.

Group F : — Premiums and Reserves (Chapters 17–18: Gross premiums, Gross premium reserves)

Once a product is designed, an insurer needs to know two things: what to charge (the premium) and how much money to set aside to meet future claims (the reserve). These chapters teach the calculations behind both — effectively, the actuarial version of a business plan, where the “gross” premium accounts for all expenses and profit loading, not just the theoretical cost of the risk.

Group G : — Multiple Lives and Contingent Benefits (Chapters 19–22: Joint life and last survivor benefits, Contingent and reversionary benefits, Mortality profit, Competing risks)

Real insurance products often depend on more than one life — think of a joint life policy on a married couple, or a benefit that only pays if a specific dependent survives the policyholder (contingent/reversionary benefits — the basis of most family pension products). Mortality profit examines what happens when actual deaths in a portfolio differ from what was assumed in pricing — a live risk-management concept insurers monitor every year. Competing risks extends the life table framework to situations involving more than one “decrement” — for example, an employee who might leave a pension scheme either by death, resignation, or retirement, and you need to model all three simultaneously.

Group H : — Modern Contracts and Profit Testing (Chapters 23–25: Unit-linked and conventional with-profits contracts, Profit testing, Reserving aspects of profit testing)

The final block covers unit-linked products — policies where part of the premium is invested in market-linked funds, a dominant product category in India today (ULIPs). Profit testing is the technique insurers use to project a policy’s expected cash flows year by year and check whether it will actually be profitable under realistic assumptions — essentially a detailed financial model for a single insurance contract, run before the product is ever sold. The final chapter applies this same profit-testing logic specifically to reserving decisions, closing the loop between pricing, reserving, and profitability that the whole subject has been building towards.

Exam Format

Paper A is a written/constructed-response paper in Microsoft Word (70% weighting). Paper B is an applied modelling paper in Microsoft Excel (30% weighting). Both papers are sat in the same exam sitting.

Prerequisites

No prior actuarial exams are required. A working foundation in compound interest, basic probability, and random variables is assumed.