Rule of 72: The time required to double an investment at R percent compounded annually is closely approximated by 72/R.
For example, $100 invested at 6% compounded annually would double to $200 in approximately 72 / 6 or 12 years.
The Compound Interest Formula is:
where P is the Principal invested at r, and compounded
m times per year for n years.
A is the total earned in the account after n years. Note
that r is the annual interest rate
divided by 100, but that in the Rule of 72, R is the annual
interest rate.
For Annual Compounding (where m is 1), the formula becomes:
In the example above, the actual time required for $100 to
double is 11.89 years
and can be solved in the following manner:
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But why does this Rule of 72 seem to work?
Take the Compound Interest Formula, and solve for n:
Now, take the Rule of 72 and solve for n (remember to divide
R by 100 to get r):
Graph these two functions on a graphing calculator to see why the values
of n are very close. Use the trace function and change the
domain (values for r)
and the range (values for n) to be:
XMIN = 0
XMAX = .12
XSCAL = .01
YMIN = 0
YMAX = 100
YSCAL = 10