Continuously Compounded Rule of 72 Examples

Years Rate Savings

Want to know how long it will take to double your money? Use this calculator to get a quick estimate. Simply enter a given rate of return and this calculator will tell you how long it will take for the money to double by using the rule of 72. That rule states you can divide 72 by the rate of return to estimate the doubling frequency.

Rule of 72 Formula: Years = 72 / rate OR rate = 72 / years

Years Required to Double Principal

Want to know the required rate of return you will need to achieve to double your money within a set period of time? Use this calculator to get a quick estimate. Simply enter a given period of time and this calculator will tell you the required rate for the money to double by using the rule of 72. That rule states you can divide 72 by the length of time to estimate the rate required to double the money.

Rule of 72 Formula: Years = 72 / rate OR rate = 72 / years

Required Rate of Interest

Today's Local Savings Rates

The following table shows current rates for savings accounts, interst bearing checking accounts, CDs, and money market accounts. Use the filters at the top to set your initial deposit amount and your selected products.

What is the Rule of 72?

For any given sum, one can quickly estimate the doubling period or the rate of compounding by dividing the other of the two into the number 72. It is a handy rule of thumb and is not precise, but applies to any form of exponential growth (like compound interest) or exponential decay (the loss of purchasing power from monetary inflation).

Examples

How long would it take for a person to double their money earning 3.6% interest per year?

72 / 3.6 = 20 years

How long would it take money to lose half its value if inflation were 6% per year?

72 / 6 = 12 years

Doubling Time Table

Growth Rate	Time to Double
1%	72
2%	36
3%	24
4%	18
5%	14.4
6%	12
7%	10.29
8%	9
9%	8
10%	7.2
11%	6.55
12%	6
13%	5.54
14%	5.14
15%	4.8
16%	4.5
17%	4.24
18%	4
19%	3.79
20%	3.6
21%	3.43
22%	3.27
23%	3.13
24%	3
25%	2.88
26%	2.77
27%	2.67
28%	2.57
29%	2.48
30%	2.4
31%	2.32
32%	2.25
33%	2.18
34%	2.12
35%	2.06
36%	2
37%	1.95
38%	1.89
39%	1.85
40%	1.8
41%	1.76
42%	1.71
43%	1.67
44%	1.64
45%	1.6
46%	1.57
47%	1.53
48%	1.5
49%	1.47
50%	1.44
51%	1.41
52%	1.38
53%	1.36
54%	1.33
55%	1.31
56%	1.29
57%	1.26
58%	1.24
59%	1.22
60%	1.2
61%	1.18
62%	1.16
63%	1.14
64%	1.13
65%	1.11
66%	1.09
67%	1.07
68%	1.06
69%	1.04
70%	1.03
71%	1.01
72%	1
73%	0.99
74%	0.97
75%	0.96
76%	0.95
77%	0.94
78%	0.92
79%	0.91
80%	0.9
81%	0.89
82%	0.88
83%	0.87
84%	0.86
85%	0.85
86%	0.84
87%	0.83
88%	0.82
89%	0.81
90%	0.8
91%	0.79
92%	0.78
93%	0.77
94%	0.77
95%	0.76
96%	0.75
97%	0.74
98%	0.73
99%	0.73
100%	0.72

Is the Rule of 72 Exact?

No. It has slight rounding issues, though is quite close.

The formula for annually compounded interest is P [1 + (r / n)]^(nt) where:

• P = principal
• r = annual interest rate as a decimal
• n = frequency with which interest is compounded annually
• t = term of loan or investment in years

Why 72?

The log of 2 is 0.69. For continuously compounded interest the "rule of 72" would actually technically be the rule of 69.

2P = P [1 + (r / n)]^(nt)

t = ln(2) / r

The natural log of 2 is 0.69. So you would dive 69 by the rate of return.

Most interest bearing accounts are not continuosly compouding. If you solve the above equation again and use annually compounded interest then the 0.69 mentioned above ranges between 0.697 and 0.734. 72 was chosen as a reasonable factor in part because it is easy to divide into by other numbers and it is a decent approximation for the fairly low rates of interest typically associated with savings accounts or secured consumer lending.

If one were to use credit cards with a much higher interest rate like 20% to 25% APR then the 72 would be closer to being in the 76 to 77.7 range.

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Source: https://www.calculators.org/savings/rule-of-72.php

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