Applied Mathematics

Learn Financial Mathematics (Actuarial)

The deterministic time-value-of-money core behind the actuarial FM exam and fixed-income finance: compound interest and discount, effective vs nominal rates and the force of interest δ; level, due, deferred, varying, and perpetual annuities (aₙ, sₙ, äₙ); loan amortization and the interest/principal split, sinking funds, and equations of value; bond pricing at a premium or discount, book value and amortization; yield rates via net present value and the internal rate of return, plus spot and forward rates; and interest-rate risk through Macaulay/modified duration, convexity, and immunization.

Free to start · adaptive placement finds your level · reviews timed to your own forgetting.

What you'll learn

30 lessons in Financial Mathematics (Actuarial)

Time value of money — interest, discount & the force δAnnuities — present & accumulated value of level paymentsLoan amortization — outstanding balance & the principal splitBonds — price, premium, discount & book valueYield rates — net present value & the internal rate of returnDuration & convexity — interest-rate sensitivityNominal vs effective rates — reading a rate's disguiseForce of interest — continuous compoundingAnnuity-due — paying at the start of the periodDeferred annuities — payments that start laterPerpetuities — payments that never endIncreasing & decreasing annuitiesSinking funds — repay by saving on the sideEquations of value — moving money through timeBond amortization — writing off premium & discountSpot & forward rates — the term structureModified duration — estimating the price swingImmunization — protecting a surplus from rate movesSurvival modelsLife tablesLife expectancyLife insuranceLife annuitiesNet premiumsPolicy reservesMultiple decrementsSelect and ultimate mortalityLoss severityThe aggregate loss modelCredibility theory
How Erudia teaches

Built to be understood — and remembered.

Every idea is taught with motivation and a worked example before the drills, and an FSRS spaced-repetition engine schedules each review for the day its model predicts you would forget it. A short placement check finds what you already know, so you start Financial Mathematics (Actuarial) exactly where it's useful.

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