When analyzing the effects of differences in economic growth rates over time, it is generally the case that seemingly small differences in annual growth rates result in large differences in the size of economies (usually measured by Gross Domestic Product, or GDP) over long time horizons. Therefore, it's helpful to have a rule of thumb that helps us quickly put growth rates into perspective. Show
One intuitively appealing summary statistic used to understand economic growth is the number of years it will take for the size of an economy to double. Fortunately, economists have a simple approximation for this time period, namely that the number of years it takes for an economy (or any other quantity, for that matter) to double in size is equal to 70 divided by the growth rate, in percent. This is illustrated by the formula above, and economists refer to this concept as the "rule of 70." Some sources refer to the "rule of 69" or the "rule of 72," but these are just subtle variations on the rule of 70 concept and merely replace the numerical parameter in the formula above. The different parameters simply reflect different degrees of numerical precision and different assumptions regarding the frequency of compounding. (Specifically, 69 is the most precise parameter for continuous compounding but 70 is an easier number to calculate with, and 72 is a more accurate parameter for less frequent compounding and modest growth rates.)
For example, if an economy grows at 1 percent per year, it will take 70/1=70 years for the size of that economy to double. If an economy grows at 2 percent per year, it will take 70/2=35 years for the size of that economy to double. If an economy grows at 7 percent per year, it will take 70/7=10 years for the size of that economy to double, and so on. Looking at the preceding numbers, it is clear how small differences in growth rates can compound over time to result in significant differences. For example, consider two economies, one of which grows at 1 percent per year and the other of which grows at 2 percent per year. The first economy will double in size every 70 years, and the second economy will double in size every 35 years, so, after 70 years, the first economy will have doubled in size once and the second will have doubled in size twice. Therefore, after 70 years, the second economy will be twice as big as the first! By the same logic, after 140 years, the first economy will have doubled in size twice and the second economy will have doubled in size four times- in other words, the second economy grows to 16 times its original size, whereas the first economy grows to four times its original size. Therefore, after 140 years, the seemingly small extra one percentage point in growth results in an economy that is four times as large.
The rule of 70 is simply a result of the mathematics of compounding. Mathematically, an amount after t periods that grows at rate r per period is equal to the starting amount times the exponential of the growth rate r times the number of periods t. This is shown by the formula above. (Note that the amount is represented by Y, since Y is generally used to denote real GDP, which is typically used as the measure of the size of an economy.) To find out how long an amount will take to double, simply substitute in twice the starting amount for the ending amount and then solve for the number of periods t. This gives the relationship that the number of periods t is equal to 70 divided by the growth rate r expressed as a percentage (eg. 5 as opposed to 0.05 to represent 5 percent.)
The rule of 70 can even be applied to scenarios where negative growth rates are present. In this context, the rule of 70 approximates the amount of time it will take for a quantity to be reduced by half rather than to double. For example, if a country's economy has a growth rate of -2% per year, after 70/2=35 years that economy will be half the size that it is now.
This rule of 70 applies to more than just sizes of economies- in finance, for example, the rule of 70 can be used to calculate how long it will take for an investment to double. In biology, the rule of 70 can be used to determine how long it will take for the number of bacteria in a sample to double. The wide applicability of the rule of 70 makes it a simple yet powerful tool. This graph’s smooth curve shows how an investment, economy, population, or any other quantity will grow at a constant rate of interest or growth—that is, at a constant percentage. In this case the percentage is 2.8 percent, compounded annually. In the graph, in year 0 the value is 1. Soon, though, the value is twice as high, rising to 2. It doubles again to 4, doubles again to 8, and again to 16. An economy or investment growing at 2.8 percent per year will double every 25 years. Thus, it will double 4 times in a century: 2, 4, 8, 16. There is a very useful tool for quickly calculating the doubling time for a given growth rate: the Rule of 70. If you know the percentage growth rate and want to know how long it will take an initial value to double, simply divide 70 by the rate. In this case, 70 divided by 2.8 = 25. The value doubles every 25 years and therefor increases 16-fold in 100 years. By the Rule of 70 we can calculate that a growth rate of 7 percent will cause an initial value to double in just 10 years. China’s economy has been growing by more than 7 percent since the early 1990s. If a value—the size of China’s economy, for example—doubles every 10 years, it will go through 10 doublings in a century: 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024. If China’s economy maintained a 7 percent growth rate for a century it would become more than 1,000 times larger. It is important to recall such facts the next time the Dow or some other economic indicator falls on the news that Chinese growth has “slowed” to 7 percent or less. The rule of 70 is a way to estimate how many years it takes for a person's money or investment to double. Typically, the rule of 70 is a calculation to help determine the number of years it might take to double the money with a specific rate of return. This rule is often used to compare investments when they have different annual interest rates compounded. That way, it's easy to find out how long it would take to see the investment quickly grow. Sometimes, financial investors refer to the rule of 70 as doubling time.  The FormulaWhat is the rule of 70? It requires a specific formula. You divide 70 by the annual rate of return to get the number of years it would take to see the investment double in size. How to Calculate this Rule of 70
What Does This Tell an Investor?The rule of 70 helps investors determine the value of their investment right now and what it might be in the future. While this is a rough estimate, the rule can be very effective. It's easier to figure out how many years it would take for that investment to double in size. Investors can easily use such a metric to evaluate different investments. These can include the growth rate for a person's retirement portfolio or mutual fund returns. For example, a calculation yielded the result of 15 years before the portfolio doubles in size. The investor prefers for that result to be close to 10 years instead. Therefore, they could make suitable allocation changes to their portfolio to increase the investment's growth rate. The rule is ultimately accepted as the way to manage various exponential growth concepts without having to use complex mathematical procedures. Typically, it is related to the items within the financial sector to examine the investment and its potential growth rate. When the number "70" is divided by the expected annual rate of growth or the return on financial transactions, the estimate in years is produced. Limitations for the Rule of 70Typically, the rule of 70 works very well. However, the answer received isn't completely accurate for various reasons. For one, it assumes that something is compounded continuously. Therefore, the interest is constantly calculated and then added to the account. Most savings accounts end up compounding interest monthly instead of constantly. Even a regular CD is only compounded once a month, so it's not truly continuous. This happens because there's usually a set interest rate, and the investor doesn't touch it for the term's length. With that, the rule of 70 slightly underestimates how many years it takes for the it to grow. The difference isn't noticeable with a small annual growth rate, but it becomes apparent when dealing with higher rates, such as 10 percent or more. This is significant if the investor is estimating investment growth, such as mutual funds or stocks. Changing the account balance can also change those calculations, especially if there are large withdrawals or deposits within the time period. The rule of 70 assumes a constant growth rate for the investment's lifespan. Most savings accounts aren't going to change the interest rate, but that can happen. Year after year, an investment or stock portfolio can have a different annual rate of growth and return. Therefore, it's nearly impossible to predict it for the next year. It's best to recalculate regularly as the annual rate of return changes. In a sense, the rule of 70 and the rules to double it include estimates of the growth rates or rates of return on investments. Therefore, inaccurate results are possible. Considerations for Rules 69 and 72Sometimes, people can use the rule of 69 and the rule of 72. The function is similar for these as with the rule of 70. However, it uses 69 or 72 in place of 70 for the calculations. Ultimately, the rule of 69 is more accurate when focused on continuous compounding double time. Still, 72 might be more accurate for compounding intervals that happen less frequently. There is a various number of years that can be used for doubling time. Other Applications for the Rule of 70The rule of 70 has other useful applications, as well. It is possible to determine how long it might take for a country's real GDP (gross domestic product) to double. This is similar to calculate the compound interest rates. Use the GDP growth rate as the divisor for the rule of 70. For example, the growth rate in China is at 10 percent. With the rule of 70, it predicts that it might take seven years for the real GDP in China to double (70/10). Rule of 70 vs. Real GrowthIt is essential to remember that this rule of 70 is just an estimate based on various forecasted growth rates. If the growth rate fluctuates, the original calculation might prove to be inaccurate. The US population was estimated at just 161 million in 1953. In 2015, it doubles to 321 million. The growth rate in 1953 was listed as just 1.66 percent. With the rule of 70, the population should have doubled by 1995. Since there were changes to the growth rate, it lowered the average rate, so the rule of 70 was inaccurate. Though the rule of 70 isn't a precise estimate, the equation does provide some guidance when handling compounding interest issues and exponential growth. That can be applied to any instrument that sees steady growth expected for the future and the long-term. For example, population growth with time is a great one. However, the rule of 70 isn't applied well for instances where growth rates are anticipated to vary significantly. Takeaways So Far
Examples for the Rule of 70An investor wants to review their retirement portfolio to determine how long it might take to double it, given the various rates of return. The investment options made can be useful for future value and are related to growth rates. Here are various calculations on this rule based on different growth rates:
The Difference Between the Rule of 70 and Compound InterestCompound interest is calculated from the initial principal. This includes accumulated interest from previous periods on the loan or deposit. Typically, the rate for compound interest depends on its frequency. When the number of compounding periods is higher, there is more compound interest on the future investment. It is essential to calculate the compound interest for doubling time. That way, the number of years is known, and so is the value of the investment. Ultimately, with this rule, the investment doubles in size depending on how the interest is compounded. Bottom Line for Minimizing Investment TaxesThe bottom line here is that people must take a strategic approach to investing to maximize retirement income and minimize taxes. In most cases, the investment can see great returns, but it's hard to determine doubling time without using the rule of 70. It's a good idea to get a personal financial advisor to help, especially when investing a large sum such as $200,000. It could be stressful wondering how to invest 200k and they can help with that stress. With that, they should not take commissions or be given financial incentives. That way, the personal advisor is on the investor's side and isn't just out to make money. Sometimes, investors can get a free consultation with a personal financial advisor. That way, they determine if that person is the right fit. Though it's good to find personal service at a low price, it is essential to choose someone who cares about you and offers the services required. Economics plays a huge part in the world right now, and personal finance is essential. Growing a nest egg isn't easy. However, with practice and the right insights, growing personal finances is a possibility. While math might not a strong suit for most people, the world of finance is not going away. Practice frugal money-saving tips, invest with the right companies for the best results, and educate yourself on financial terms such as nominal fee. Disclosures: Securities offered through LPL Financial, member FINRA/SIPC. Investment advice offered through Stratos Wealth Partners, LTD., a registered investment advisor. Stratos Wealth Partners, LRD. The Kelley Financial Group, LLC are separate entities from LPL Financial. This information is not intended to be a substitute for specific individualized tax or legal advice. We suggest that you discuss your specific situation with a qualified tax or legal advisor. Content in this material is for general information only and not intended to provide specific advice or recommendations for any individual. The content is developed from sources believed to be providing accurate information. No investment strategy assures a profit or protects against loss. Investing in mutual funds involves risk, including possible loss of principle. Fund Value will fluctuate with market conditions and it may not achieve its investment objective. There is no guarantee that a diversified portfolio will enhance overall returns or outperform a non-diversified portfolio. Diversification does not protect against market risk. The Standard & Poor’s 500 Index is a capitalization weighted index of 500 stocks designed to measure performance of the broad domestic economy through changes in the aggregate market value of 500 stocks representing all major industries. Contributions to a traditional IRA may be tax deductible in the contribution year, with current income tax due at withdrawal. Withdrawal prior to age 59 ½ may result in a 10% IRS penalty tax in addition to current income tax. A Roth IRA offers tax deferral on any earnings in the account. Qualified withdrawals of earnings from the account are tax-free. Withdrawals of earnings from the account are tax-free. 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