Force of Interest Calculator

About this calculator

The force of interest, denoted δ (delta), is the continuously compounded equivalent of a stated effective interest rate, defined as δ = ln(1 + i) where i is the effective annual rate. It represents the instantaneous rate at which money grows at every single moment rather than at discrete annual, monthly, or daily compounding intervals, and it's the rate that appears inside continuous-compounding formulas like A = Pe^(δt).

This calculator converts an effective annual interest rate into its force of interest. Actuaries use δ constantly in life contingency and annuity valuation formulas where continuous compounding simplifies the math, and finance students and quants use it to move between nominal, effective, and continuously compounded rate conventions when pricing bonds or derivatives.