CM1 Actuarial Mathematics
The foundation of every actuarial career: compound interest, life contingencies, and cash-flow modelling.
About CM1
CM1 is the first paper most students sit. It builds the mathematical foundation that every subsequent actuarial paper depends upon: compound interest, present values, life tables, mortality models, and the pricing of insurance products. Master CM1 and you have proven to every employer that you can handle actuarial mathematics.
Who is this for?
Students who have completed A-level Maths or equivalent (Class 12 with strong Maths). No prior actuarial knowledge needed, because this is where every actuarial career begins.
151 days until CM1, April 2027
CM1A 12 Apr · CM1B 14 Apr · entry closes in 85 days
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Learn CM1 free — 15 worked explainers
One idea per page, explained from scratch, each ending in a worked example with the arithmetic shown in full. These are the ideas students most often get stuck on in CM1. Start anywhere.
- Simple and compound interest, and the principle that rules out one of them Accumulate money under simple and compound interest, state the principle of consistency, and show by calculation that simple interest breaks it while compound interest cannot
- Present value, the discount factor, and why d is not i Calculate a present value using a discount factor, convert between the rate of interest and the rate of discount in both directions, and find the true rate of interest earned on a commercially discounted bill
- Nominal rates payable p times a year, and the loan that costs more than it says Convert a nominal rate payable p times a year into an effective annual rate and back, and find the effective rate a flat-rate instalment loan is really charging
- Force of interest explained, and how it relates to i, v and d Convert between an effective rate, a nominal rate, the force of interest and a discount factor, and check the answer is in the right order
- When the interest rate changes: steps, and a force that varies Accumulate and discount a cashflow through step changes in the interest rate and under a variable force of interest, and find the equivalent constant rate over the whole period
- Continuous payment streams, and why they are worth more than they look Calculate the present value of a continuous payment stream at a constant force of interest and under a force that changes, and explain why it exceeds the annual annuity by the ratio of i to delta
- Annuity functions in CM1: immediate, due, deferred and temporary Write down the present value of a stream of level payments using the right annuity function, and check it two ways
- Perpetuities and increasing annuities: payments that never stop, or never stay level Value a level perpetuity, a perpetuity-due, an arithmetically increasing annuity and a geometrically growing perpetuity, and say when a growing perpetuity has no finite value
- Money rates, real rates and inflation: the exact link, not the subtraction Convert between a money rate of interest and a real rate using the exact relationship, say in which direction the usual subtraction errs, and accumulate a sum in both money and real terms
- Real yields from an inflation index, and index-linked payments Deflate a series of cashflows using inflation index values, find the real yield on an index-linked investment, and show that the money-terms and real-terms calculations agree exactly
- Loan schedules: the prospective and retrospective methods Find the outstanding capital on a loan two independent ways and split an instalment into interest and capital
- Life table functions explained: l(x), d(x), q(x) and p(x) Read any single-life mortality probability directly off a life table and check it a second way
- Net premiums and the equivalence principle, worked from first principles Calculate a net premium from a life table and an interest rate using the equivalence principle
- Reserves in CM1: prospective, retrospective, and why they agree Calculate a policy reserve both prospectively and retrospectively and state when the two must agree
- Thiele's differential equation, explained term by term Read every term in Thiele's differential equation and solve it numerically with a recursive step
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Complete Syllabus
- Time value of money: compound interest, present values, accumulations, force of interest
- Equation of value: solving for unknown interest rates, time periods, yields
- Annuities: immediate, due, deferred, increasing and decreasing annuities, perpetuities
- Loan schedules: prospective and retrospective methods, interest and capital components
- Life tables: mortality rates, survival functions, qₓ, pₓ, curtate future lifetime
- Life insurance models: whole life, term assurance, endowment, pure endowment, net single premiums
- Life annuities: whole life and temporary annuities, complete and curtate expectations of life
- Net and gross premiums: equivalence principle, expense loadings, gross premium prospective reserve
- Reserves: prospective and retrospective reserves, Thiele’s differential equation
- Multiple decrement models: competing risks, associated single decrement tables
Career Outcomes
Junior Actuarial Analyst, Trainee Actuary at any insurance company or consultancy
₹4–8 LPA with CM1 cleared
Start with compound interest and annuities. The life-table notation looks intimidating but follows a consistent pattern once you understand qₓ and pₓ.
“Ravi Sir’s approach to CM1 is completely different: he builds intuition first, formulas second. I cleared in my first attempt and my employer specifically mentioned CM1 during my interview.”