### Single Payment Interest Factors: Continuous Compounding.

The single payment compound amount formula (Equation 3-3)

If we increase

*m*, the number of compounding subperiods per year,with out limit, m becomes very large and approaches infinity,a nd r/m becomes very small and approaches zero.

This is the condition of continuous compounding, that is, where the duration of the interest period decreases from some finite duration Δt to an infinitely small duration dt, and the number of interest periods per year becomes infinite. In this situation of continuous compounding:

To find compound amount and present worth for continuous compounding and a single payment, we write:

Square brackets around the factors distinguish continuous compounding. If your hand calculator does not have e

**^x**, use the table of e

**^rn**and e

**^-rn**, provided at the end of the appendix

**containing the compound interest tables.**

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