Happy Financial Independence Day! How Long Will It Take to Double Your Money?
Posted July 5th, 2016.
Categories: The Calculating Lawyer.
The 4th of July is a perfect day to think about your independence — your financial independence, that is! So, what if you wanted to double, or triple or even quadruple your money. How long would it take to do that? There’s a handy formula for figuring it out in a matter of seconds. All you need to know is the secret number — 72.
If you’re a lawyer or a business leader advising a client, the Rule of 72 is a useful technique for estimating how long it will take to double a client’s money, and to restore them to a position of financial power after suffering a financial loss. The magic of 72, however, does not provide a scientifically perfect calculation for doubling one’s money, but rather an estimate, in years, of the doubling time of an investment.
The formula is 72/r where r equals a fixed rate of return. So, for example, if you invested $1,000 at a 4% rate of return, how many years would it take to double the investment? The approximate answer is 72/4, which equals 18. In other words, you could turn $1,000 into $2,000, if invested at 4%, in approximately 18 years. (Had you used a financial calculator, you would have determined that you could have doubled your $1,000 investment at 4% in exactly 17.673 years). For the best accuracy, the Rule of 72 should be used for interest rates ranging from 6% to 10%.
Knowing the Rule of 72 provides an easy ratio for calculating how long it could take a business client to double a capital investment or how long it might take a spouse in a divorce case to reach 100% return on a certain fund of money. Although it is not a substitute for a future value calculation or other more technical determinations, the Rule of 72 can provide quick estimates for negotiating purposes in a wide variety of case scenarios.
Tripling and Quadrupling
Applying the same mathematical logic that underlies the Rule of 72, we can establish two additional related rules: the Rule of 114 and the Rule of 144. The Rule of 114 tells us how long it would take to triple an investment of money at a particular rate of return. The Rule of 144 tells us how long it would take to quadruple the investment. Let’s try a few examples:
Let’s say you want to know how long it would take to double an investment of $100,000, to triple it, and to quadruple it, if you could obtain an 8% rate of return?
To double it, apply 72/r . The answer is 72/8 or effectively nine years to double the money.
To triple it, apply 114/r. The answer is 114/8 or 14.25 years to triple the money.
To quadruple it, apply 144/r. The answer is 144/8 or 18 years to quadruple the money.
So, you can now easily estimate that a $100,000 fund, invested at 8%, would double in nine years, triple in five years and three months thereafter, and quadruple in less than four more years.
The various rules can also be used to compare rates of return over time. For example, applying the Rule of 144, with an 8% rate of return, we see that it would take 18 years to quadruple one’s investment. What interest rate would reduce the timeline to approximately 12 years? Apply some simple algebra: 144/r = 12. (In this instance, we already know the number of years, 12. What we don’t know is the rate of return, r. It is the interest rate that we’re looking for).
To solve for “r”, multiply both sides by r. Your resulting equation is now 144 = 12r. Then divide both sides by 12. Thus: r = 12. And there’s your answer! A rate of 12% would therefore be necessary to quadruple the $100,000 investment in 12 years.
