# Doubling Time Formula

Last Updated :

21 Aug, 2024

Blog Author :

Edited by :

Ashish Kumar Srivastav

Reviewed by :

Dheeraj Vaidya, CFA, FRM

Table Of Contents

## What is Doubling Time?

Doubling time refers to the time period required to double the value or size of investment, population, inflation etc and is calculated by dividing the log of 2 by the product of number of compounding per year and the natural log of one plus the rate of periodic return.

##### Table of contents

- The doubling time formula is a mathematical calculation that estimates the time required for investment, population, or another variable to double in value or size.
- The doubling time formula is based on the concept of exponential growth. Therefore, it assumes a constant growth rate over time.
- The doubling time formula is typically used in finance and economics to assess the growth rate or compounding of investments or to analyze population growth or other similar phenomena.
- The doubling time formula is derived from the compound interest formula and can be applied to various situations where exponential growth is observed.

### Doubling Time Formula

Mathematically, the doubling time formula is represented as,

**Doubling Time = ln 2 /**

where

- r = rate of annual return
- n = no. of compounding period per year

In the case of continuous compounding formula, the calculation of doubling time in terms of years is derived by dividing the natural log of 2 by the rate of annual return (since (1 + r/n) ~ e^{r/n}).

**Doubling time = ln 2 / **

**= ln 2 /****= ln 2 / r**

where r = rate of return

The above formula can be further expanded as,

**Doubling time = 0.69 / r**** = 69 / r% **which is known as rule of 69.

However, the above formula is also modified as the rule of 72 because practically continuous compounding is not used, and hence 72 gives a more realistic value of the time period for less frequent compounding intervals. On the other hand, there is also the rule of 70 in vogue, which is used just for the ease of calculation.

### Doubling Time Calculation (Step by Step)

Follow the below steps:

**Firstly, determine the rate of annual return for the given investment. The annual rate of interest is denoted by ‘r.’****Next, try to figure out the frequency of compounding per year, which can be 1, 2, 4, etc., corresponding to annual compounding, half-yearly, and quarterly, respectively. The number of compounding periods per year is denoted by ‘n.’ (The step is not required for continuous compounding)****Next, the rate of periodic return is calculated by dividing the rate of annual return by the number of compounding periods per year.****Rate of periodic return = r / n****Finally, in case of discrete compounding, the formula in terms of years is calculated by dividing the natural log of 2 by the product of no. of compounding period per year and the natural log of one plus the rate of periodic return as****Doubling time = ln 2 /****On the other hand, in the case of continuous compounding, the formula in terms of years is derived by dividing the natural log of 2 by the rate of annual return as,****Doubling time = ln 2 / r**

### Example

**Let us take an example where the rate of annual return is 10%. Calculate the doubling time for the following compounding period:**

**Daily****Monthly****Quarterly****Half Yearly****Annual****Continuous**

Given, Rate of annual return, r = 10%

#### #1 – Daily Compounding

Since daily compounding, therefore n = 365

Doubling time = ln 2 /

- = ln 2 /
- = ln 2 /
- = ln 2 /
- = ln 2 /
- = ln 2 / ,"answer":,"jsonQuestion":"What is the formula for calculating doubling time?","jsonAnswer":"The formula for doubling time is: Doubling time = ln(2) / (growth rate), where \u0022ln\u0022 represents the natural logarithm and the growth rate is expressed as a decimal or percentage."},{"id":"faq-question-1684948428587","question":,"answer":,"jsonQuestion":"How is the doubling time formula used in finance?","jsonAnswer":"In finance, the doubling time formula helps investors estimate how long it would take for an investment to double in value based on its growth rate. It indicates the potential growth and compounding power of an investment."},{"id":"faq-question-1684948446519","question":,"answer":,"jsonQuestion":"Can the doubling time formula be used for any growth rate?","jsonAnswer":"The doubling time formula can be used for any positive growth rate. However, it assumes a constant growth rate over time. Therefore, if the growth rate fluctuates or is unstable, the formula may provide an approximation rather than an exact doubling time."},{"id":"faq-question-1684948459566","question":,"answer":,"jsonQuestion":"What are the limitations of the doubling time formula?","jsonAnswer":"The doubling time formula assumes continuous compounding and a constant growth rate, which may not always reflect real-world scenarios. In addition, it does not account for factors such as inflation, market fluctuations, or changing economic conditions affecting the actual growth rate."}]} -->
**What is the formula for calculating doubling time?**The formula for doubling time is: Doubling time = ln(2) / (growth rate), where "ln" represents the natural logarithm and the growth rate is expressed as a decimal or percentage.

**How is the doubling time formula used in finance?**In finance, the doubling time formula helps investors estimate how long it would take for an investment to double in value based on its growth rate. It indicates the potential growth and compounding power of an investment.

**Can the doubling time formula be used for any growth rate?**The doubling time formula can be used for any positive growth rate. However, it assumes a constant growth rate over time. Therefore, if the growth rate fluctuates or is unstable, the formula may provide an approximation rather than an exact doubling time.

**What are the limitations of the doubling time formula?**The doubling time formula assumes continuous compounding and a constant growth rate, which may not always reflect real-world scenarios. In addition, it does not account for factors such as inflation, market fluctuations, or changing economic conditions affecting the actual growth rate.

### Recommended Articles

This article has been a guide to Doubling Time and its meaning. Here we learn the formula to calculate doubling time for different compounding periods along with some practical examples along with downloadable excel templates. You may learn more about excel modeling from the following articles –

- Formula of Monthly Compound Interest
- Daily Compound Interest
- Effective Annual Rate Formula
- TVM Definition

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- = ln 2 /

- = ln 2 /

- = ln 2 /