ACT 201 · Year 2 · Semester 1 · 4 credits · Actuarial

Financial Mathematics (Exam FM)

Master the time value of money, cash flow engineering, and interest rate immunisation from first principles to SOA Exam FM mastery.

Full practice exam · 30 Q · 120 min

Season 1 · 8 episodes

Solvency Horizon: The Apex Life Audit

When an unexpected interest-rate spike threatens a 1.2 billion dollar annuity block at Apex Life, junior actuary Maya Lin must master the mathematics of interest, cash flows, bond portfolios, immunisation, and swaps to save the insurer from regulatory liquidation.

Protagonist · Maya Lin, Junior Actuarial Analyst in Asset-Liability Management at Apex Life Assurance

Setting · Apex Life Assurance headquarters, Chicago, during an intensive state regulatory examination

Stakes · A 45 million dollar capital deficit across 45,000 structured settlement and retirement policies will trigger a mandatory regulatory takeover unless the asset-liability profile is fully reconciled and immunised before the State Insurance Commission deadline.

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Episodes

Season finale: Maya presents a fully immunised asset-liability framework backed by a receiver swap overlay to the board and state regulators, restoring statutory surplus and guaranteeing lifetime benefits for all 45,000 policyholders.

From the lecturer: Welcome to Financial Mathematics. This course forms the mathematical bedrock of your actuarial career: every life table in FAM, every reserve in ASTAM, and every capital model in enterprise risk management relies on the cash-flow valuation principles we build here. To get the most from these lesson-films, treat them as active workshops. Keep your Texas Instruments BA II Plus Professional calculator and a pad of grid paper beside you at all times. Before you touch a financial calculator key or write an equation of value, sketch the timeline: mapping cash flows to explicit integer and fractional time nodes eliminates the vast majority of indexation errors. We will first derive every pricing formula, duration metric, and immunisation condition analytically from first principles, and then verify them numerically using both BA II Plus keystrokes and computational scripts. This course directly prepares you for SOA Exam FM and CAS Exam 2 while instilling the Asset-Liability Management intuition required in contemporary capital markets. Pause frequently, test your recall at every checkpoint, and embrace the discipline of exact valuation.

Cold open

At 6:45 AM on a rainy Tuesday, Maya Lin arrives at her desk to find an urgent red folder marked State Insurance Department Audit. Chief Actuary David Keller drops a printout with a glaring variance: the actuarial reserve for a legacy structured settlement block differs by twelve million dollars depending on whether the valuation software uses continuous compounding, nominal rates, or annual effective rates. With the regulator arriving at noon, Maya must establish absolute mathematical precision on the force of interest.

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Transcript

Define the accumulation function and distinguish between effective rates of interest and discount.
Convert seamlessly between annual effective, nominal, and continuous compounding measures.
Compute accumulated and present values under constant and time-varying forces of interest.
Apply equivalence relationships to solve fundamental actuarial pricing and reserving problems for SOA Exam FM.