Rule of 70

Dispelling the Myth

You may have heard of the rule of 72.  It’s a simple way of determining how long it takes to double your money, given the interest rate.  For example, with a rate of 6%, it takes 12 years to double your money and with a rate of 12%, it takes 6 years.  I set out to prove this theory and since I was dealing with mortgage investments and payments are made on a monthly basis, I compounded monthly and here’s what I found.At a rate of 1%, compounded monthly, $100,000 reaches $200,000 in 832 months or 69.3 years.  Multiply the number of years by the rate and you get 69.3 and that’s our constant.  In other words, the product of rate and years (that it takes to double) will be fairly constant.  You can see by the ‘Constant’ column that it varies and isn’t really constant, at all, but since it’s fairly close to 70 and increases steadily, as the rate of return increases, let’s just call this a constant and derive a simple rule for figuring out how long it will take to double our money, at a given rate of return.  At 5%, it takes 14 years and at 14%, it takes 5 years.  At 7%, it takes 10 years and at 10%, it takes 7 years.  Emerging from the data, is a constant of approximately 70.  So, the next time someone mentions the Rule of 72, just smile, because you know better.  When you invest in a mortgage instrument, where payments are made monthly, the compounding is monthly and the rule of 72 doesn’t work because, the constant is closer to 70.  Let’s call this the Rule of 70 and keep it a secret, O.K.?

Rate Start Finish Months Years Constant pct
1 $100,000 $200,000 832 69.3 69.3 0.01
1.5 $100,000 $200,000 555 46.2 69.4 0.015
2 $100,000 $200,000 416 34.7 69.4 0.02
2.5 $100,000 $200,000 333 27.8 69.4 0.025
3 $100,000 $200,000 278 23.1 69.4 0.03
3.5 $100,000 $200,000 238 19.8 69.4 0.035
4 $100,000 $200,000 208 17.4 69.4 0.04
4.5 $100,000 $200,000 185 15.4 69.4 0.045
5 $100,000 $200,000 167 13.9 69.5 0.05
5.5 $100,000 $200,000 152 12.6 69.5 0.055
6 $100,000 $200,000 139 11.6 69.5 0.06
6.5 $100,000 $200,000 128 10.7 69.5 0.065
7 $100,000 $200,000 119 9.9 69.5 0.07
7.5 $100,000 $200,000 111 9.3 69.5 0.075
8 $100,000 $200,000 104 8.7 69.5 0.08
8.5 $100,000 $200,000 98 8.2 69.6 0.085
9 $100,000 $200,000 93 7.7 69.6 0.09
9.5 $100,000 $200,000 88 7.3 69.6 0.095
10 $100,000 $200,000 84 7.0 69.6 0.1
10.5 $100,000 $200,000 80 6.6 69.6 0.105
11 $100,000 $200,000 76 6.3 69.6 0.11
11.5 $100,000 $200,000 73 6.1 69.6 0.115
12 $100,000 $200,000 70 5.8 69.7 0.12
12.5 $100,000 $200,000 67 5.6 69.7 0.125
13 $100,000 $200,000 64 5.4 69.7 0.13
13.5 $100,000 $200,000 62 5.2 69.7 0.135
14 $100,000 $200,000 60 5.0 69.7 0.14
14.5 $100,000 $200,000 58 4.8 69.7 0.145
15 $100,000 $200,000 56 4.6 69.7 0.15
15.5 $100,000 $200,000 54 4.5 69.8 0.155
16 $100,000 $200,000 52 4.4 69.8 0.16
16.5 $100,000 $200,000 51 4.2 69.8 0.165
17 $100,000 $200,000 49 4.1 69.8 0.17
17.5 $100,000 $200,000 48 4.0 69.8 0.175
18 $100,000 $200,000 47 3.9 69.8 0.18
18.5 $100,000 $200,000 45 3.8 69.8 0.185
19 $100,000 $200,000 44 3.7 69.9 0.19
19.5 $100,000 $200,000 43 3.6 69.9 0.195
20 $100,000 $200,000 42 3.5 69.9 0.2
20.5 $100,000 $200,000 41 3.4 69.9 0.205
21 $100,000 $200,000 40 3.3 69.9 0.21
21.5 $100,000 $200,000 39 3.3 69.9 0.215
22 $100,000 $200,000 38 3.2 69.9 0.22
22.5 $100,000 $200,000 37 3.1 70.0 0.225
23 $100,000 $200,000 37 3.0 70.0 0.23
23.5 $100,000 $200,000 36 3.0 70.0 0.235
24 $100,000 $200,000 35 2.9 70.0 0.24
24.5 $100,000 $200,000 34 2.9 70.0 0.245
25 $100,000 $200,000 34 2.8 70.0 0.25
25.5 $100,000 $200,000 33 2.7 70.0 0.255
26 $100,000 $200,000 32 2.7 70.1 0.26
26.5 $100,000 $200,000 32 2.6 70.1 0.265
27 $100,000 $200,000 31 2.6 70.1 0.27
27.5 $100,000 $200,000 31 2.5 70.1 0.275
28 $100,000 $200,000 30 2.5 70.1 0.28
28.5 $100,000 $200,000 30 2.5 70.1 0.285
29 $100,000 $200,000 29 2.4 70.1 0.29
29.5 $100,000 $200,000 29 2.4 70.2 0.295
30 $100,000 $200,000 28 2.3 70.2 0.3
30.5 $100,000 $200,000 28 2.3 70.2 0.305
31 $100,000 $200,000 27 2.3 70.2 0.31
31.5 $100,000 $200,000 27 2.2 70.2 0.315
32 $100,000 $200,000 26 2.2 70.2 0.32
32.5 $100,000 $200,000 26 2.2 70.2 0.325
33 $100,000 $200,000 26 2.1 70.3 0.33
33.5 $100,000 $200,000 25 2.1 70.3 0.335
34 $100,000 $200,000 25 2.1 70.3 0.34
34.5 $100,000 $200,000 24 2.0 70.3 0.345
35 $100,000 $200,000 24 2.0 70.3 0.35
35.5 $100,000 $200,000 24 2.0 70.3 0.355
36 $100,000 $200,000 23 2.0 70.3 0.36
36.5 $100,000 $200,000 23 1.9 70.4 0.365
37 $100,000 $200,000 23 1.9 70.4 0.37
37.5 $100,000 $200,000 23 1.9 70.4 0.375
38 $100,000 $200,000 22 1.9 70.4 0.38
38.5 $100,000 $200,000 22 1.8 70.4 0.385
39 $100,000 $200,000 22 1.8 70.4 0.39
39.5 $100,000 $200,000 21 1.8 70.4 0.395
40 $100,000 $200,000 21 1.8 70.46 0.4