# Is Doubling Time with Continuous Compounding Useful in ROI Analysis

Doubling Time w/t Continuous Compounding = ln(2) ÷ r

r = rate

Doubling time with continuous compounding is utilized todetermine the time required to double an investment using continuouscompounding interest rate. With this equation, a person takes the productof natural log with 2 and then divide the figure with the rate of return.

The doubling time formula quickly returns the time in years,months or days to double the investment but it depends on the rate which youare using for calculation. If the rate is on a monthly basis then the resultwill be in months if you are using annual rate then the result will also be inyears.

This formula is used for continuous compounding investments while on the other side the simple interest double time formula is different. If you are not sure which formula to use then simply use doubling time to determine the targeted time for making your investment double.

## Doubling time with continuous compounding example

Let suppose that an individual is looking to calculate thetime which is required to double the investment. The rate of interest is 7% andit is continuously compounded. There is no need to get aware of the investmentamount or principal because the formula can calculate the figures without that.

Now here is a slightly tricky part, if one needs tocalculate the result in months then the rate of return (interest rate) must beconverted to a monthly basis. Now putting values in doubling time withcontinuous compounding formula;

Doubling time with continuous compounding = ln(2) ÷ 0.07

Doubling time with continuous compounding = 9.9 years

## How doubling time with continuous compounding formula induced

This formula is derived by using the continuous compoundingformula, if we look on the formula individually then it looks like;

FV = PV × ert

In the equation above FV denotes to future value, PV topresent value and e is themathematical constant. While on the other side is for rate and tis for the time period. As we need the future value double to present value so,we can rewrite the equation as;

2 = ert

We can rewrite the formula as;

2 = (er)t

Because we are solving for t, so we will slightlyadjust the formula above according to our needs as;

t = ln(2) ÷ ln(er)

This formula can then be converted into the equation whichis presented on top of this page.

To understand this concept first we have to look in thesimple interest formula;

S = P (1 + rt)

Adding the assumption of doubling the investment to the aboveequation, and we get;

2 = 1 + rt

Now if we subtract 1 from both sides of the equation,then we get;

1 = rt

Because doubling time formula focuses on the timeessentially, that’s why we can divide both sides with rate and get the resultssame as available on top of the page.