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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
= Pert
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
= Pert
2 = ert
, ln 2 = rt,
t = ln 2
/ r
If we
multiply the top and bottom by 100, the previous equation can be
re-written 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 yearsThe 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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