Very useful approximation to quickly estimate amount of time the money will double given interest
rate is “Rule of 72”
Table 2.1: “Rule of 72” Compared with the Exact Solution R a t e 72
Rate ____________________________________________________________________________________________________________________________________________________ (1 + Rate∕100) 72
Rate _________________________________________________________________________________________________________________________________________________________________ 1
log 2 (1+Rate∕100) ______________ 1 % _________________________________________________________________________________________________________________________________________________ 7 2 _________________________________________________________________________________________________________________________________________________ 2 . 0 4 7 _________________________________________________________________________________________________________________________________________________ 6 9 . 6 6
2 % 3 6 2 . 0 3 9 3 5 . 0 0 ___________ 3 % _________________________________________________________________________________________________________________________________________________ 2 4 _________________________________________________________________________________________________________________________________________________ 2 . 0 3 3 _________________________________________________________________________________________________________________________________________________ 2 3 . 4 5
4 % 1 8 2 . 0 2 6 1 7 . 6 7 ___________ 5 % _________________________________________________________________________________________________________________________________________________ 1 4 . 4 _________________________________________________________________________________________________________________________________________________ 2 . 0 1 9 _________________________________________________________________________________________________________________________________________________ 1 4 . 2 1
6 % 1 2 2 . 0 1 2 1 1 . 9 0 ___________ 7 % _________________________________________________________________________________________________________________________________________________ 1 0 . 2 8 _________________________________________________________________________________________________________________________________________________ 2 . 0 0 6 _________________________________________________________________________________________________________________________________________________ 1 0 . 2 4
8 % 9 1 . 9 9 9 9 . 0 1 ___________ 9 % _________________________________________________________________________________________________________________________________________________ 8 _________________________________________________________________________________________________________________________________________________ 1 . 9 9 2 _________________________________________________________________________________________________________________________________________________ 8 . 0 4
1 0 % 7 . 2 1 . 9 8 6 7 . 2 7
As you can see in Table 2.1 , this approximation is pretty good for practical purposes, with error increasing towards
high rates and rates close to zero.