The ultimate of compounding periods is instantaneous, or continuous, compounding over the investment horizon (period). In this case the present value formula becomes:

PV = FVt [1/(1 + r/∞)]n∞ = FVn(e−rn)

where n is the number of years in the investment horizon (period). Thus, in Example 2–5, if the annual interest rate on the investment is 16 percent compounded continuously, the present value of the $10,000 investment in six years is:

PV = $10,000(e−0.16×6) = $10,000(0.382893) = $3,828.93