Formula and Use
The simple interest doubling time formula is used to work out the amount of time (n) it takes to double the value of a lump sum investment allowing for simple interest at a given discount rate (i%). Simple interest is a type of interest calculation where the interest earned is based solely on the original principal amount and does not compound over time.
Simple Interest Doubling Time Formula Example 1
If an investment of 400 is made at the start of period one and earns simple interest at a discount rate of 20%, then the number of periods it takes to double the value of the investment is given by the simple interest doubling time formula as follows:
n to double = 1 / i n to double = 1 / 20% = 1 / 0.20 n to double = 5 periods
Additionally the calculation of the doubling time can be seen in the table below.
| Period | Start | Interest | End |
|---|---|---|---|
| 1 | 400 | 80 | 480 |
| 2 | 480 | 80 | 560 |
| 3 | 560 | 80 | 640 |
| 4 | 640 | 80 | 720 |
| 5 | 720 | 80 | 800 |
As can be seen the simple interest calculated at 20% on the investment of 400 is the same each period. Consequently at the end of five periods, the investment has doubled to 800, which is the same answer given by the simple doubling time formula.
Simple Interest Doubling Time Formula Example 2
It is important to realize that the rate (i) is the rate per period. So for example if the rate (i) is for a year then the calculated periods (n) will be in years
To illustrate suppose an investment earns interest at a rate of 5% a year. In this case the number of years it takes to double the investment is given by the formula as follows
n to double = 1 / i n to double = 1 / 5% = 1 / 0.05 n to double = 20 years
It is important to realize that the simple interest doubling time formula assumes that the interest rate (i) remains constant throughout the investment period and does not account for changes in the interest rate or inflation. Additionally, the formula only applies to investments that earn simple interest and does not take into account the effects of compounding.
The simple doubling time formula is one of many used in time value of money calculations, discover another at the links below.
About the Author
Chartered accountant Michael Brown is the founder and CEO of Double Entry Bookkeeping. He has worked as an accountant and consultant for more than 25 years and has built financial models for all types of industries. He has been the CFO or controller of both small and medium sized companies and has run small businesses of his own. He has been a manager and an auditor with Deloitte, a big 4 accountancy firm, and holds a degree from Loughborough University.