10.7 Simple Future and Present Values: Continuous Compounding (Supplemental)

In order to solve for continuous compounding, we must engage the “rule of limits” or otherwise utilize the “natural log.” The natural logarithm is the logarithm to the base e, where e is equivalent to the irrational number 2.71828. The following presents an exemplary solution for continuous compounding. 

 

FV = PV (e Rn)

and

PV = FV (e -Rn)

 

Where,      e      = 2.71828

                 R      = interest rate

Note:

P is omitted since the compounding is continuous rather than periodic.

 

 

Example:         PV      = $1

       R        = .09

       N        = 10 years

       FV      = ?

 

Solution:         FV      = ($1) (2.71828 (.09) (10) )

                                   = $2.4596

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Introduction to Financial Analysis Copyright © 2022 by Kenneth S. Bigel is licensed under a Creative Commons Attribution 4.0 International License, except where otherwise noted.

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