## Continuous compounding, Financial Accounting

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In Section we had established an association among the effective and nominal rate of interest where compounding arise n times a year that is as given:

r = (1 +  k/m )m - 1

Rearranging equation a10, this can be specified as:

r = [(1 +  k/(m/k))m/k ]k- 1

Let us substitute m/k by x from Eq (a11)

r = [(1 + 1/x )k] - 1

In continuous compounding ∞ → m that implies ∞ →∞  in Eq 12. = e = 2.71828...

By equation (a12) results in

R = ek-1

⇒ (r + 1) =  ek

Thus the future value of an amount when continuous compounding is done is as follows:

FVn = PV * ekm

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