Doubling Time Formula

This is a simple calculator I made for determining the amount of time it will take for an investment to multiply in value (ie. double, triple, or quadruple) based on the interest rate gained. This calculation is based on two entries. First, the calculator needs to know what multiple is desired (d). If you want to know how long something will take to double, enter a value of 2. (To calculate time to triple enter a d of 3, quadruple enter a d of 4, etc). Then all it needs is the interest rate per term (r). The number of terms at that interest rate required for the value of the investment to reach the specified multiple (d) in value is the result (n). The actual formula used for this calculation can be seen in the image that accompanies this paragraph.

In case you were wondering, the amount initially invested has no affect on doubling time or any other multiple.

As an example, say I open a bank CD with $10,000 at an interest rate of 4.5% annually and I want to know how long it will take for that CD to be worth $30,000. In other words, I want to know how long it will take to triple in value. To get the answer I enter 4.5 for r and 3 for d. The calculator then tells me it would take nearly 25 years (~24.96) for that $10,000 to grow to $30,000 at that interest rate! However, most bank CDs pay interest monthly or quarterly. To get an accurate result in such a situation, you would first have to compute your term interest rate. Following the above example, say the interest was paid monthly. That means each month the CD would appreciate 4.5%/12, or 0.375%. That is what you'd need to enter in the calculator and it would then tell you the number of months it would take for the CD to triple in value (293.51). To convert the number of months back to a number of years I of course just divide that result by 12 and end up with 24.46 years. (That's a difference of about 6 months compared with my original calculation based on annual interest accrual.) Of course, if you are instead dealing with quarterly interest accrual you just divide the annual interest by 4 and then divide the resultant time (n) by 4 to convert the result back to years (24.55 years using my example numbers).

This calculator's results can serve as a basis to compare two or more potential investments. It will show you that a typical bank account with an interest rate of 2% will take 35 years to double in value. On the other hand, an investment in stocks with their long-term average gain of 10.8% per year will take just shy of seven years to double in value. Of course, the trade-off for that is the higher risk of loss associated with stock investments (you're never guaranteed a 10.8% return)! But I believe that a diversified stock investment in the only way to go if you are investing for a period of ten years or more.

You may have also heard of the Rule of 70 or 72 (some disciplines use 70 while others use 72). That rule states if you divide your interest/growth rate (expressed as a percentage) into 70/72 the result will be the number of terms it will take for your investment/population to double. Although this may seem easier to calculate, it is not nearly as accurate as the formula I use in this calculator (and steadily increases in its inaccuracy as the interest rate increases; try a 70% or 100% interest rate for example).

Note that the interest rate (r) must be expressed as a percentage (ex. 4.5%). Do not include the percentage sign. The calculator will properly convert the percentage into a proportion by dividing your entry by 100. And yes, you can also enter a fractional value for the multiple (ie. 1.5 if you want to know how long $1,000 will take to reach $1,500 in value).

Interest rate(r) - %:	Time to d (n):
Multiple (d):