From Colin’s comment on Hacker News, the Rule of 72 works because it’s on the “right side” of 100*ln(2). This gives a value of 3.5 years, indicating that you'll have to wait an additional quarter to double your money compared to the result of 3.27 years obtained from the basic Rule of 72. Can you see why a population growth rate of 3% vs 2% could be a huge problem for planning? For 14% rate of return, it would be the rule of 74 (adding 2 for 6 percentage points higher), and for 5% rate of return, it will mean reducing 1 (for 3 percentage points lower) to lead to the rule of 71. That is the after-tax compound annual rate of return he would have to earn to meet his desired objective. For example, the rate of 11% annual compounding interest is 3 percentage points higher than 8%.

We want to use R as an integer (3) rather than a decimal (.03), so we multiply the right hand side by 100: There’s one last step: 69.3 is nice and all, but not easily divisible. For example if you wanted to double an investment in 5 years, divide 72 by 5 to learn that you'll need to earn 14.4% interest annually on your investment for 5 years: 14.4 × 5 = 72.

View desktop site, Use the rule of 72 to calculate how long it takes a country's real GDP per capita to double under the following growth rates. The geometric mean is the average of a set of products, the calculation of which is commonly used to determine the performance results of an investment or portfolio. Rule of 72. First, let's start with how to use the Rule of 72 when you have an estimated rate of return you'll earn on your investments. (Do NOT press Enter after typing the answer in each cell.

It is a useful rule of thumb for estimating the doubling of an investment.

It is used for calculating interest on investments where the accumulated interest is not added back to the principal. The most important property of the number e is related to the slope of exponential and logarithm functions, and it's first few digits are 2.718281828. This convenience makes it easier to use the Rule of 72 for a close approximation of compounding periods. The Rule of 72 applies to cases of compound interest, and not to the cases of simple interest.

Joshua Kennon co-authored "The Complete Idiot's Guide to Investing, 3rd Edition" and runs his own asset management firm for the affluent. The chart below compares the numbers given by the Rule of 72 and the actual number of years it takes an investment to double.

Use Tab or take the cursor to the next cell.) For example if you wanted to double an investment in 5 years, divide 72 by 5 to learn that you'll need to earn 14.4% interest an… This gives: The Rule of 72 is more accurate if it is adjusted to more closely resemble the compound interest formula—which effectively transforms the Rule of 72 into the Rule of 69.3. The calculation of a country's GDP takes into … The rule of 70 is a way of estimating the time it takes to double a number based on its spread rate. The more often the interest is compounded, the greater the return will be. To estimate a rough rate of return required to achieve such a feat, she'd use this version of the Rule of 72 and divide 72 by 12.

To estimate a rough rate of return required to achieve such a feat, he'd use this version of the Rule of 72 and divide 72 by 4. (Rule of 72 calculator: features/rule72.htm a. If the interest per quarter is 4%, then it will take (72 / 4) = 18 quarters or 4.5 years to double the principal. The formula is useful for understanding the effect of compound interest. At 6% interest, your money takes 72/6 or 12 years to double. If you pay 15% interest on your credit cards, the amount you owe will. If inflation decreases from 6% to 4%, an investment will be expected to lose half its value in 18 years, instead of 12 years. “If you can't explain it simply, you don't understand it well enough.” —Einstein (. An APR is defined as the annual rate charged for borrowing, expressed as a single percentage number that represents the actual yearly cost over the term of a loan.

The basic rule of 72 says the initial investment will double in 3.27 years.

So, suppose we have \$1 and a yearly interest rate R. After one year we have:1 * (1+R)For example, at 10% interest, we’d have \$1 * (1 + 0.1) = \$1.10 at the end of the year. Gross domestic product (GDP) is one of the most common indicators used to track the health of a nation's economy. The result, 18, represents 18%. Use the rule of 72 to calculate how long it takes a country's real GDP per capita to double under the following growth rates. All rights reserved. The natural logarithm is the amount of time needed to reach a certain level of growth with continuous compounding. t = 72 ÷ R. You can also calculate the interest rate required to double your money within a known time frame by solving for R: (Enter only the numerical values in the blanks.) Half the fun in using this magic formula is seeing how it’s made. The formula is interest rate multiplied by the number of time periods = 72: Commonly, periods are years so R is the interest rate per year and t is the number of years. Imagine that an investor that knows they can earn 12% on their money in a given real estate investment. It contrasts with simple interest where the investor withdraws the interest every month and keeps the principal amount consistent leading to comparatively lower returns. By not withdrawing the interest every month, the investor is increasing the principal value which helps him earn more interest. The Rule of 72 is a simplified version of the more involved Answer 1: John would take 72 divided by 7. The unit does not necessarily have to be invested or loaned money. For maximum accuracy—particularly for continuous compounding interest rate instruments—use the Rule of 69.3. The result, 6, represents 6% compounded annually. Here’s the formula: Years to double = 72 / Interest Rate This formula is useful for financial estimates and understanding the nature of compound interest. Now, imagine that a widowed retiree wants to double her wealth in twelve years.

As you use bigger rates, the accuracy will get worse. Not too hard, right? Instead of needing to double your capacity in 36 years, you only have 24. Use the Rule of 72 to estimate how long it will take to double an investment at a given interest rate. Without adding any additional cash to her current balance, what rate of return must she earn in order to graduate with \$10,000 in her account? For example, say you have a very attractive investment scheme offering a 22% rate of return. While calculators and spreadsheet programs like excel sheets have inbuilt functions to accurately calculate the precise time required to double the invested money, the Rule of 72 comes in handy for mental calculations to quickly gauge an approximate value. 72 is closeby, and has many more factors (2, 3, 4, 6, 12…).

& If you invest a sum of money at 6% interest per year, how long will it take you to double your investment? Half the fun in using this magic formula is seeing how it’s made. If you invest a sum of money at 0.5% interest per month, how long will it take you to double your investment? In the case of compound interest, the interest is calculated on the initial principal and also on the accumulated interest of previous periods of a deposit. The annual percentage yield (APY) is the effective rate of return on an investment for one year taking into account the effect of compounding interest.

(Do NOT press Enter after typing the answer in each cell. If growth increases to 4%, the economy doubles in 18 years. The period given by the logarithmic equation is 3.49, so the result obtained from the adjusted rule is more accurate. It is a handy rule of

If inflation is 6%, then a given purchasing power of the money will be worth half in around (72 ÷ 6) = 12 years.

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