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# Do You Know the Rule of Doubling Your Money?

31 March 2016

### Key Takeaways

• The rule of 72 is a mathematical shortcut that estimates how long it takes to double your money.
• Divide the number 72 by the annual rate of return you expect on an investment. The result is the approximate number of years it takes to double your money.
• Use the rule of 72 to compare investments and plan for large expenses.

Doubling your money sure has a nice ring to it. But how long does it take? It can take around 10 years if you invest in stocks based on a historical average return of 7 percent.1 If you had invested in the SPDR S&P Dividend ETF (SDY) around July 22, 2009 following one of the worst financial disasters in our lifetime, you would have doubled your money by now.

How you invest can greatly impact the amount of time it takes to double your money. You can slog it out for 72 years if your cash is just sitting in a savings account or CD. Why is there such a vast difference compared to stocks? Let’s explore the math.

### The Perks of Compounding

First, it is important to grasp the concept of compounding. In essence, compounding refers to generating earnings from previous earnings. As an investment grows, the rate of return is calculated on a larger base. The opposite occurs if an investment is in decline.

For example, let’s say you invest \$10,000 in a stock that rises in price by 10 percent in year one. In other words, your \$10,000 grows to \$11,000 at the end of the first year. Happy with a \$1,000 gain, you decide to keep the investment. The stock rises another 10 percent in year two. At the end of the second year your total investment is now worth \$12,100. Even though the stock rises 10 percent in both years, your investment appreciates an additional \$100 in year two. Why? Your year two returns are calculated on a larger base, \$11,000 versus \$10,000.

Compounding can be tricky to calculate in your head, however, unless you’re a math whiz. The good news is you can use a mathematical shortcut called the “rule of 72” to quickly estimate how long it takes an investment with a fixed annual return to double in size.

Rule of 72: divide the number 72 by the annual rate of return you expect on an investment. The result is the approximate number of years it takes to double your money.2

Now let’s see why it can take 10 years to double your money in stocks versus 72 years in a savings account. If you invest \$10,000 and earn a respectable seven percent a year, it takes about 10 years to get to \$20,000.

72 / 7 = 10.28 years

Savings accounts and CDs, on the other hand, still earn close to bupkis these days. A savings account offered by a national bank currently yields 0.75 percent APY3 while a 12-month CD yields 1.05 percent APY.4 Depositing \$10,000 with, say, a 1 percent rate of return – which is below the Fed’s target rate of two percent inflation – takes about 72 years to double.5 Wow, that’s a mighty long time compared to 10 years for stocks to double!

72 / 1 = 72 years

Of course the stock market does not provide a fixed rate of return every year. Use the rule of 72 for ballpark estimates. Your actual results can vary but historically stocks have been a more efficient way to grow wealth.

### Estimate Large Expenses With the Rule of 72

To help you plan for your future expenses, you can also use the rule of 72 to estimate them. Let’s say you welcome a baby into your clan. How much is her college education going to cost?

First, research shows the projected annual increase in college tuition and fees is between three to four percent.5 Now use the rule of 72 to estimate how long it may take for tuition costs to double.

At an annual cost increase of three percent, tuition costs can double in 24 years.

72 / 3 = 24 years

If prices go up four percent a year, however, tuition can double in 18 years.

72 / 4 = 18 years

Let’s assume a four percent annual cost increase in our example since a baby born today should be ready to enter college 18 years from now.

Second, let’s examine the cost of college today. According to The College Board, in-state costs average \$9,410 for tuition and fees, and \$10,138 for room and board totaling \$19,548 for 2015-16. Private, not-for-profit schools average \$32,405 for tuition and fees, and \$11,516 for room and board totaling \$43,921. Public school expenses for out-of-state students fall in between.

Let’s use an initial cost of \$32,000 per year. Applying a subsequent four percent increase in cost each year results in an approximate cost of \$135,886 for a student entering a 4-year college today.

Year 1: \$32,000
Year 2: \$33,280
Year 3: \$34,611
Year 4: \$35,995

Total: \$135,886

Lastly, double the above total to get a rough idea of how much your baby’s college education expenses will be in 18 years: \$271,772. That’s quite a difference!

Once you estimate how much money you may need for the big expenses down the road, work on an investment plan to pay for them.

For example, let’s say you find an investment earning 12 percent a year. If you invest about \$34,000 today, your bundle of joy will have an ample college fund by the time she’s 18. What’s the math? The rule of 72 says you can double your money in six years with a 12 percent annual return. Work backwards from \$272,000 and then halve your money for each six-year period. This means you would need about \$136,000 saved by year 12, \$68,000 by year six and \$34,000 today. Nifty!

There are many other ways to use the rule of 72 as well. You can estimate how long it can take your home’s value to double. Or you can use the rule of 72 to calculate the potential impact of inflation on your savings. At a two percent annual rate of inflation, assuming your cash is not earning any interest, your savings can halve in about 36 years. A three percent rate of inflation halves your money in 24 years, a four percent rate at 18 years, etc.

### The Rule Of 72’s Imperfections

It’s important to remember that most investments do not provide fixed rates of returns. In addition, the rule of 72 does not account for investment fees or capital gains taxes. It’s also helpful to note that rates of return between the range of six and 10 percent work best with the rule of 72. Curious math geeks seeking further information can read Stanford’s complex explanation on the numbers.

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1. Maverick, J.B, “What Is The Average Annual Return For The S&P 500?” Investopedia, 2016.
2. Investopedia Staff, “Rule Of 72,” Investopedia, 2016.
3. Capital One, “Current Rates,” Capital One Financial Corporation, March 25, 2016.
4. Ally Bank, “Compare CDs,” Ally Financial Inc., March 25, 2016.
5. Board of Governors Of The Federal Reserve System, “Why Does The Federal Reserve Aim For 2 Percent Inflation Over Time?” The Federal Reserve, January 26, 2015.
6. The College Board, “Average Rates Of Growth Of Published Charges By Decade,” The College Board, 2016.
Tags: rule of 72
1. Alisa
15 Apr at 4:06 pm

You know it’s funny. I’d heard about this rule before but never took the time to figure out what it was for or how it works. Thanks for explaining it so well. What a difference higher returns make when you look at the numbers this way. They should really teach this in high school. If I had seen these charts when I was a teen I think I would jumped into the stock market way earlier than I did.