Every investor wants to grow his wealth by as much as possible in the shortest period of time. The time span required to double your money would depend on the returns or interest rate earned on your investments. Obviously, higher the interest or return on your investment, faster will your money double. You can very easily find out the time your investments would take to double your money using a DIY formula called 'the rule of 72'. Show Rule of 72 is a simple formula where you divide the number '72' with the interest rate offered by your investment instrument to get an idea on how soon can you double your money with that particular investment. For an instance, a bank FD offering an interest rate of 5% p.a., will take over 14 years to double your money. The formula is applied as below: Rule of 72 =72/5 = 14.4 years How much returns should your investments generate if you want to double your money? Alternatively, by tweaking the formula a bit, you can find out returns required to double your money in a specific period. Let's find out: If you want to double your money in three years, your investments should earn between 21% to 24% (72/3 years) every year. Similarly, if you want to double your money in five years, your investments will need to grow at around 14.4% per year (72/5). If your goal is to double your invested sum in 10 years, you should invest in a manner to earn around 7% every year. Rule of 72 provides an approximate idea and assumes one time investment. Time to double money under PPF, Sukanya Samriddhi Yojana, KVP, NSC, NPS and mutual funds We have taken the current interest rates or returns offered by these instruments. PPF at an annual interest rate of 7.1% will take around 10 years to double your money assuming the interest rate remains at 7.1% (72/7.1 =10.14). Similarly, Sukanya Samriddhi Yojana will take around 9.4 years to double your money at the current interest rate of 7.6%. KVP will take 10.4 years to double your money at the current interest rate of 6.9%. National Savings Certificates at 6.8% interest rate will take 10.5 years to double your investments. NPS Scheme C, Scheme G of Tier II account are giving on an average 11.5% returns in the one year period. Assuming similar performance, NPS will take 6.2 years to double your investments. Short duration mutual funds and dynamic bond funds at present are giving around 8.5% returns in the last one year. Assuming similar returns, these instruments will take 8.4 years for your investments to double. Debt medium to long duration mutual funds at 8.7% returns p.a, will take 8.3 years to double your investments. Catch all the Business News, Market News, Breaking News Events and Latest News Updates on Live Mint. Download The Mint News App to get Daily Market Updates. More Less Calculating compound interest is complicated. Luckily, there’s a simple shortcut that helps you estimate how a fixed interest rate will affect your savings: the Rule of 72. The BasicsThe Rule of 72 is a tool used to estimate how long it will take an investment to double at a given interest rate, assuming a fixed annual rate of interest. All you need to use the tool is an interest rate, which means you can make estimates for your current account rate or use this rule to know what rate you should look for if you want to double your money by a specific deadline. To figure out how long it will take to double your money, take the fixed annual interest rate and divide that number into 72. Let’s say your interest rate is 8%. 72 ∕ 8 = 9, so it will take about 9 years to double your money. A 10% interest rate will double your investment in about 7 years (72 ∕ 10 = 7.2); an amount invested at a 12% interest rate will double in about 6 years (72 ∕ 12 = 6). Using the Rule of 72, you can easily determine how long it will take to double your money. To figure out what interest rate to look for, use the same basic formula, but run it backward: divide 72 by the number of years. So if you want to double your money in about 6 years, look for an interest rate of 12%. The basic algebraic formula looks like this, where Y is the number of years and r is the interest rate: Y = 72 ∕ r and r = 72 ∕ Y This rule works for interest rates from about 4% up to about 20%; after that, the error becomes significant and more straightforward math is required.  Illustration: Chelsea Miller Why 72?Here, we merely scrape the surface of that “more straightforward math.” To really dive deep into why the rule works, check out this article. The Rule of 72 is itself an estimation. It uses a concept called natural logarithms to estimate compounding periods. In mathematics, the natural logarithm is the amount of time needed to reach a particular level of growth using continuous compounding. For math enthusiasts out there: it is easiest to see how this works through continuously compounded interest. (The Rule of 72 addresses annually compounded interest, but we’ll get there in a minute.) When dealing with continuously compounding interest, you can work out the exact time it takes an investment to double by using the time value of money formula (TVM) and simplifying the equation until eventually, you are left with something like this: ln(2)= rY The natural log (ln) of 2 is about 0.693. Solve for interest rate (r) or number of years (Y), and then multiply by 100 to express as a percentage or year, respectively. Click here to read how this tool works, and for disclaimers. Click here to read how this tool works, and for disclaimers. Wait...If our new formula is based on the number 69.3 (0.693 × 100), that begs the question: Why isn’t it called the Rule of 69.3? First, that just doesn’t sound quite as good as “The Rule of 72.” Second, there are two points to remember:
The math equation for fixed annual interest is slightly more complex, and simplifying it leaves us with approximately 72.7. Normally, we would round up to 73. However, 72 is much easier to work with, as it is readily divisible by 2, 3, 4, 6, 8, 9, and 12. As we are already estimating, convenience wins out, and we are left with the Rule of 72. HistoryThe Rule of 72 was first introduced in the late fifteenth century by the Franciscan friar and Italian mathematician Luca Pacioli. A contemporary of Leonardo da Vinci, Pacioli is considered by many to be the father of accounting. The Rule of 72 was introduced in his book Summa de arithmetica, geometria, proportioni et proportionalita, published in 1494 for use as a textbook for schools in what is now northern Italy. How long will it take money to double itself if invested at 10% compounded annually?A 10% interest rate will double your investment in about 7 years (72 ∕ 10 = 7.2); an amount invested at a 12% interest rate will double in about 6 years (72 ∕ 12 = 6). Using the Rule of 72, you can easily determine how long it will take to double your money.
What is 10 percent compounded annually?Simple interest is when interest is gained only on the principal amount. In this scenario, interest earned is not reinvested. If you were to gain 10% annual interest on $100, for example, the total amount earned per year would be $10.
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