Part III — Actuarial Applications

Fixes core TVM vocabulary and the equation of value, builds validated tools such as accumulated_value and present_value, and sets the concept → math → code → tool → agent pattern the rest of Part III follows.

Annuity-immediate and annuity-due, perpetuities, m-thly and continuous annuities, arithmetic and geometric annuities, and Newton-Raphson for solving an unknown rate.

Treats a loan as an annuity viewed from the other side: outstanding balance by the prospective and retrospective methods, interest/principal decomposition, and amortisation schedules with drop or balloon payments.

Composes the existing loan tools for refinancing decisions and covers NPV, IRR, comparing alternatives, and the multiple-IRR pitfall.

Derives the bond price formula as a coupon annuity plus a redemption lump sum, book value, premium/discount amortisation, and solving for yield.

Prices a callable bond to guarantee a minimum yield by checking every candidate call date, and shows where the common "premium bonds are called early" heuristic fails.

Derives Macaulay and modified duration and convexity, and the first- and second-order approximations they give for a bond's price change.

Generalises single-rate discounting to a full yield curve: the spot/forward rate relationship, and constructing a curve one maturity at a time.

Cash flow matching, Redington immunisation's three conditions, and full immunisation, built by composing Chapter 15's duration and convexity tools.