XPost: alt.economics

Visualized: How Long Does it Take to Double Your Money?

Since 1949, the S&P 500 has doubled in value 10 times. We show how long
it takes to double your money across a range of annualized returns.

Published 5 days ago on September 14, 2023
By

Dorothy Neufeld
Visualized: How Long Does it Take to Double Your Money?
Visualized: How Long Does it Take to Double Your Money?
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At first glance, a 7% return on your investment may not seem that
impressive. Yet what if you heard that your money could double in
roughly 10 years?

The above graphic takes the rule of 72 shortcut and uses the more
precise logarithmic formula to show how long it takes to grow your money
at different annualized returns.

Why it Pays to Know the Math
Using the classic rule of 72, an investor can estimate how long it takes
to double their money. At 7% annual returns, an investor would see
$10,000 grow to $20,000 in about a decade by taking 72 and dividing it
by 7%, the rate of return.

While the rule of 72 serves as a guide to estimating when your money
will double, the more accurate way to arrive at this number is through a logarithmic equation.

In short, it divides the natural log of 2 by the natural log of 1 and
adds this to the rate of return. We can see in the table below how leads
to different results from the rule of 72:

Show
10
entriesSearch:
Rate of Return Rule of 72
# of Years to Double Money Logarithmic Formula
# of Years to Double Money
2% 36.0 35.0
3% 24.0 23.5
4% 18.0 17.7
5% 14.4 14.2
6% 12.0 11.9
7% 10.3 10.2
8% 9.0 9.0
9% 8.0 8.0
10% 7.2 7.3
11% 6.5 6.6
Showing 1 to 10 of 19 entriesPreviousNext
Consider if an investor put their money in the S&P 500. Historically, it
has averaged 11.5% returns between 1928 and 2022. In 6.4 years, their
money would double, assuming these average returns.

If they were to put this money in a savings account, where the average
savings rate is 0.6%, it would take 120 more years for their money to
reach this potential.

In real terms, which takes inflation into account, an investor would see
their money lose value if they parked it in a savings account.
Historically, inflation has averaged 3.3% over the last century.

Historical Asset Returns
Here’s how often different assets double, based on historical returns
between 1928 and 2022:

Asset Average Annual Return
1928-2022 # of Years to
Double Money End Value of $100 Invested
1928-2022
3-Month T Bill +3.32% 21.22 $2,140.51
Real Estate +4.42% 16.03 $5,121.52
U.S. T Bond +4.87% 14.58 $7,006.75
Gold +6.48% 11.04 $8,866.76
Corporate Bonds* +6.96% 10.30 $46,379.53
S&P 500** +11.51% 6.36 $624,534.55
Source: NYU Stern. *Represents Baa corporate bonds, which are considered investment grade. **Includes reinvested dividends.

We can see that 3-month T-Bills, often considered among the safest
assets, doubled about every 21 years. Often, investors consider this a
place to put cash that is low-risk and highly liquid.

Interestingly, real estate assets had returns of 4.4%, doubling roughly
every 16 years. Between 1928 and 2022, the value of $100 invested in
real estate assets would be worth $5,121.52. By contrast, the value of
$100 invested in the S&P 500, including reinvested dividends, would have reached over $624,000.

Data from NYU Stern shows that the S&P 500 has doubled about 10 times
since 1949—through recessions and bull markets—illustrating the power of investing over the long run.

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