How many years does it take before
your investment doubles in value? If we assume the investment
is compounding continuously, then we can start with the following
formula:
A
= Pe^{rt}
where
A is the
accumulated value, P
is principal, r
is the annual interest rate and t
is time in years. A doubling of the principal means that
A = 2P
and the formula would become:
2P
= Pe^{rt}
2 = e^{rt}
, ln 2 = rt,
t = ln 2
/ r
If we
multiply the top and bottom by 100, the previous equation can be
rewritten as:
t
= 100 ln 2 / 100 r
= 70 / 100 r
= 70 / annual interest rate
since
100 ln 2 ~ 70 and r
is the annual interest as a decimal, 100r
is the annual inflation as a percent. The above formula is often
called the Rule of 70. Let's consider some examples.
Example 1
Assume that the annual rate of inflation is 2.5%. Estimate the
number of years it takes for prices to double.
t
= 70 / 2.5 =
28 years
It
takes roughly 28 years for prices to double at an annual inflation
rate of 2.5%.
Example 2
You invest your savings account at 8% annual interest. How
long does it take before that original investment will double in
value using the Rule of 70?
t
= 70 / 8.0 = 8.75 ~ 9 years The online calculator below determines the
time (in years) that it takes before your investment will double in
value.
Change the annual
interest rate to the right and then click Calculate. 


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