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

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## 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:

Rate of Return Rule of 72
# of Years to Double Money
Logarithmic Formula
# of Years to Double Money
2%36.035.0
3%24.023.5
4%18.017.7
5%14.414.2
6%12.011.9
7%10.310.2
8%9.09.0
9%8.08.0
10%7.27.3
11%6.56.6
12%6.06.1
13%5.55.7
14%5.15.3
15%4.85.0
16%4.54.7
17%4.24.4
18%4.04.2
19%3.84.0
20%3.63.8

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:

AssetAverage 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.

## Mapped: The Income a Family Needs to Live Comfortably in Every U.S. State

Families in expensive states require over \$270,000 annually to live comfortably.

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## The Income a Family Needs to Live Comfortably in Every U.S. State

This was originally posted on our Voronoi app. Download the app for free on iOS or Android and discover incredible data-driven charts from a variety of trusted sources.

Families in the top five most expensive U.S. states require an annual income exceeding \$270,000 to live comfortably.

This visualization illustrates the income necessary for two working adults with two children to maintain a comfortable lifestyle in each state.

“Comfortable” is defined as the income needed to cover a 50/30/20 budget, with 50% allocated to necessities like housing and utilities, 30% to discretionary spending, and 20% to savings or investments.

The calculations for family income needed in each state were done by SmartAsset, using the cost of necessities sourced from the MIT Living Wage Calculator, last updated on Feb. 14, 2024.

## Massachusetts Tops the List

Massachusetts is the most expensive state to live comfortably in, requiring a total family income of about \$301,184. Hawaii (\$294,611) comes in second, followed by Connecticut (\$279,885).

Housing is one main reason Massachusetts is an expensive state to live in, particularly in the Boston area. In addition, the state also has a high cost of living, including expenses such as healthcare and utilities.

RankStateIncome for 2 working adults raising 2 children
1Massachusetts\$301,184
2Hawaii\$294,611
3Connecticut\$279,885
4New York\$278,970
5California\$276,723
7Washington\$257,421
8Oregon\$257,338
9New Jersey\$251,181
10Rhode Island\$249,267
11Vermont\$248,352
12Minnesota\$244,774
13New Hampshire\$244,109
15Maryland\$239,450
17Virginia\$235,206
18Illinois\$231,962
19Arizona\$230,630
20Pennsylvania\$230,464
21Maine\$229,549
22Delaware\$228,966
23Wisconsin\$225,056
24Utah\$218,483
25Michigan\$214,490
27Georgia\$212,826
28Montana\$211,411
28Iowa\$211,411
30Idaho\$211,245
31North Carolina\$209,331
31Ohio\$209,331
33Florida\$209,082
34Indiana\$206,003
35New Mexico\$203,923
36Wyoming\$203,424
37Missouri\$202,259
38North Dakota\$202,176
39Texas\$201,344
40South Carolina\$200,762
41Kansas\$196,768
42Tennessee\$195,770
43Oklahoma\$194,106
44Alabama\$193,606
45South Dakota\$192,608
46Kentucky\$190,112
47Louisiana\$189,613
48West Virginia\$189,363
49Arkansas\$180,794
50Mississippi\$177,798

Meanwhile, Mississippi is the least expensive state for a family to live comfortably, requiring \$177,798 per year. Arkansas (\$180,794) comes in second, followed by West Virginia (\$189,363). In common, all these states share low prices of housing.