Percentage & Rate Toolkit
Percentage operations, nominal ↔ effective interest rates, conversion between compounding bases (including continuous), and solving for the number of payments. Covers §7.1–7.4 of the engineering-economics material.
Percentage Operations
Nominal ↔ Effective Rate
A nominal annual rate r compounded m times per year is really (1 + r/m)ᵐ − 1 per year.
How Many Payments?
Solve for n in the standard annuity relations — saving toward a future value, or paying off a present loan.
Rates only compare on the same footing. 12% compounded monthly ≠ 12% effective — it is 12.6825% effective. Convert everything to the effective annual rate first, then judge.