Simple and Compound and Continuous Interest Calculator

Enter 3 out of 4 below
Accumulated Value Principal Interest Time

Given an accumulated balance of 3, principal of 1, and interest rate of 5.3%, calculate the Time using Continuous Interest

The formula for Accumulated Value using continous interest is:
Accumulated Value = Pert where e = 2.

Divide each side of the equation by A
A
P
=
Pert
P

Cancelling P on the right side, we get:
ert =A
P

Take the natural log of both sides of the equation Note: Ln(A/B) = Ln(A) - Ln(B):
Ln(ert) = Ln(A) - Ln(P)
rt = Ln(A) - Ln(P)

Divide both sides of the equation by r:
rt
r
=
Ln(A) - Ln(P)
r

Canceling the r on the left side, we get:
t =Ln(A) - Ln(P)
r

Plugging in our values that we entered, we get:
t =Ln(3) - Ln(1)
0.053

t =1 - 0
0.053

t =1
0.053

Time using Continuous Interest = 20.7285