Long time back, I wrote a post on the calculations behind the rule of 72 with regards to estimating the time it takes to double your initial investment. The focus of that post was to understand exactly how the rule of 72 works and whether it is accurate for all rates of return (ROR). I did not explicitly show the answer to question “how long will it take to double your money at a given rate of return?”. That’s what I will do in this post by giving you a lookup table…just look up the rate of return/interest on your investment and see how many years it will take to double the initial amount (without any additional contributions to the initial investments). Of course, you could use the rule of 72 as a rough estimate..but the table below is far more accurate, and I wanted to do this in spite of the rule of thumb.

To get this lookup table, I have used this relation between time and rate of return (read here for details on how this formula is derived from compound interest formula):

In this formula, ** t** is the time in years and

*is the rate of return (rate of interest) in decimal form (5.10% => 0.051). Since I have assumed that the frequency of compounding is annual,*

**r****becomes analogous to APY if you are considering a savings account (or a CD). Graphically, this is what the formula tells us about how much time it will take to double the initial investment:**

*r*Here is the corresponding lookup table (rounded to the nearest number of months):

Another quick and crude way to estimate the time is to “double rate and half time”- meaning, if you double your rate of return (interest rate), it will take half as much time to double your money. For example, at 1% interest rate it takes about 70 years to double your initial investment, so at twice the interest rate (2%) it will take about 70/2 = 35 years; and if you double it once more (4%) it will take about 35/2 = 17.5 years.

I should point it out (although mathematically it is very obvious) that the graphical representation is very instructive. A rise of rate of return from 1% to 4% (a difference of 3%) has a drastic effect on reducing the time (from about 70 years to about 17.5 years), however, a rise from 17% to 20% (again a difference of 3%) reduces the time from 4 years and 5 months to just 3 years and 10 months. Instinctively, I think the risk increases much more rapidly in going from 17% to 20% than in going from 1% to 4%. I am almost tempted to overlap the above graph with some kind of risk curve (towards pointing out some sort of a *comfort zone*), but I was not able to find enough information on risk-return relationship. I will appreciate any input in this matter.

I am also trying to generate a similar (but more useful) lookup table that will incorporate regular additional investments on top of the initial principal amount….that would prove to be an useful tool to convince some people to save money..as in “*look…saving just $X.XX per month will double your money is Y.YY years!*”

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Alex Gierus03.26.07 at 6:35 pmLook up “Efficient Frontier” in a finance book. It will tell you all the different rates of return and risks that are equal so that you can see the relationship between risk and return.

The other table you are talking about create, with periodic investments, is called an annuity (or perpetuity if it goes on forever). Formula can be found in any finance book or on Internet.

golbguru03.26.07 at 7:00 pmAlex: Thanks much. Found what I was looking for.

Chris B.04.03.07 at 5:18 amI was looking at the table and realized how important getting 6% compared to 4% would be. In 35 years, your money would double 3 times at 6% return per year and only 2 times with 4% return per year. Every percentage point is so important.

Jerry Corrodi03.13.09 at 6:58 amI have a stock that pays dividends monthly. APY is 14.5%. I see on your chart, it would take about 5 years, < 3 months to double, compounded annually, but what about compounding monthly (1/12 dividend/mo)? Thanks.

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