I am often surprised that many people I come across in my real estate travels are not familiar with this very helpful math rule. It is not complicated. It does not require knowledge of advanced calculus or any other high level math. But it can change your life. OK that might seem a little dramatic but for me it has been very beneficial.
I would argue it is one of the 1st steps in deciding on an investment strategy or at least to better understand what your hurdle rate needs to be. The rule of 72 is a very simple way to estimate (very precisely) how long it will take to double your investment at a given interest rate (annual return).
An early reference to the rule is in the Summa de arithmetica (Venice, 1494. Fol. 181, n. 44) of Luca Pacioli (1445–1514). He presents the rule in a discussion regarding the estimation of the doubling time of an investment, but does not derive or explain the rule, and it is thus assumed that the rule predates Pacioli by some time.
| “ | A voler sapere ogni quantita a tanto per 100 l’anno, in quanti anni sarà tornata doppia tra utile e capitale, tieni per regola 72, a mente, il quale sempre partirai per l’interesse, e quello che ne viene, in tanti anni sarà raddoppiato. Esempio: Quando l’interesse è a 6 per 100 l’anno, dico che si parta 72 per 6; ne vien 12, e in 12 anni sarà raddoppiato il capitale. (emphasis added). | ” |
Roughly translated:
| “ | In wanting to know of any capital, at a given yearly percentage, in how many years it will double adding the interest to the capital, keep as a rule
[the number] 72 in mind, which you will always divide by the interest, and what results, in that many years it will be doubled. Example: When the interest is 6 percent per year, I say that one divides 72 by 6; 12 results, and in 12 years the capital will be doubled. |
Knowing how often your investments will double at a given interest rate is a great mental tool to analyze if the risk/reward of an investment fits your life/goals. The basic breakdown is as follows:
Annual Rate : Years to Double Investment (approximate)
1% : 72 Years (and banks are actually paying most people less then this today. How can you win?)
2% : 36 Years
3% : 24 Years
4% : 18 Years
5% : 14.5 Years
6% : 12 Years (a very reasonable goal in my opinion based on 17 years of investing)
7% : 10.3 Years
8% : 9 Years
9% : 8 Years (notice the inverse relationship between rate and time)
10% : 7.2 Years
11% : 6.5 Years
12% : 6 Years
I stop at 12% for purposes of this discussion but the rule carries on much further. Most people would be ecstatic if they could earn a 12% return on their money in a safe predictable manner. If you are in your 20’s or 30’s this all but guarantees you would have enough money to retire. So how do you earn each of these rates of return while managing your risk???