Quantitative Mechanics of Periodic Compounding
Compound interest represents the generation of financial returns on prior returns combined with original principal. When recurring periodic additions are integrated, total future value \(A\) is derived from the compound interest formula paired with the future value of an ordinary annuity:
A = P × (1 + r/n)nt + PMT × [((1 + r/n)nt − 1) / (r/n)]
Where P = Principal, r = Nominal Annual Return, n = Compounding frequency per year, t = Duration in years, and PMT = Monthly addition.
The Fisher Purchasing Power Deflator
Nominal dollar totals frequently obscure purchasing power degradation. With a persistent 2.5% inflation rate, real purchasing power decays via \(Real = \frac{Nominal}{(1 + i)^t}\). At 2.5% CPI over 25 years, a nominal $500,000 portfolio confers approximately $269,760 in baseline purchasing power.