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The Rule of 72 is a simple, helpful rule for calculating the number of years it will take to double your money at a certain annual rate of return.
INSTRUCTIONS: Enter the following:
- (r) Interest rate (rate of return on investment)
Doubling Period (R72): The calculator estimates the number of periods to double one's investment.
The Math / Science
This formula approximates the period to double one's investment based on the earning percentage (r) per period. The result is the number of periods in the same units (e.g. years for 5% per year) as the period unit for the rate of return. This serves as a quick comparison for evaluating investments.
So for example, if the interest rate is 10%,
72 ÷ 10 = 7.2 years it will take just over 7 years to double our money.
Here is a graph showing $1 double at different interest rates.
how does the rule of 72 exactly work
let's take the amount of money we have after investing S dollars for t years at r% interest (given as decimal) is:
A = S(1 + r)t
to find out how long it takes to double $A to $2A is:
2A = A(1 + r)t
cancellation gives us:
2 = (1 + r)t
By solving this logarithmically we get:
ln 2 = t ln(1 + r)
t=ln(1+r)ln 2
find the value of the right-hand side for different values of r. When we multiply these values by r, an interesting thing occurs − the values are very near 72.
Range Of Interest rates.
a range of typical interest rates from r = 2 through to r = 14.
Rate Years Rate × Years
2% 35.00 70.01
3% 23.45 70.35
4% 17.67 70.69
5% 14.21 71.03
6% 11.90 71.37
7% 10.24 71.71
8% 9.01 72.05
9% 8.04 72.39
10% 7.27 72.72
11% 6.64 73.06
12% 6.12 73.40
13% 5.67 73.73
14% 5.29 74.06
(rounded to 2 deciamal places)
You can observe that the values near the last columns are near 72 so we can approximate time(t) as
t= 72/r
Equivalently, we can approximate r
r=72/t
The graph of r=72/t, with the actual times for doubling our money for various interest rates from the table above.
