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

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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 eis 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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