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 = e^{k}-1
⇒ (r + 1) = e^{k}
Thus the future value of an amount when continuous compounding is done is as follows:
FV_{n} = PV * e^{km }