Luca Pacioli

The Rule of 72 and the GMAT

The rule of 72 is quite important in the GMAT for the fast estimation of an investment doubling time. I am proud to discover it was an Italian mathematician, Luca Pacioli (1445-1514), a Franciscan friar, to publish it for the first time in Summa de Arithmetica (Venice, 1494. Fol. 181, n. 44).

” 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.”

A few provisions shall be mentioned about the applicability of this rule:

1. The rule of 72 applies to one-time investments: It can’t be applied if money is invested on a regular basis, such as monthly or yearly.

2. The rule of 72 assumes a constant annual return: it’s not applicable to stocks, mutual funds, or bonds with inherent variable return.

3. The rule of 72 is an approximation: the rule gives the best results for interest rates between 4% and 18%; outside this range, other approximations, e.g. 70 or 69, work better (e.g., to the limit of continuous compounding, 69 gives the best result at any rate)

Beware of the power and the limits of the Rule of 72, especially when you sit for a GMAT test session! A good source of information is the Wikipedia’s page on the Rule of 72.

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