How to Ask Rich People for Money

How to Ask Rich People for Money.

Fundraising for charity is an important part of any nonprofit group's work. In the U.S. alone, donors gave almost $287 billion in 2011. Many people who work for nonprofits feel uncomfortable asking donors for money, but without their help most nonprofit groups would not be able to carry out their missions. Learning how to effectively and respectfully ask wealthy individuals for money can help you ensure your charity or favorite nonprofit, federally recognized as 501 (c) (3), group prospers and is able to help those in need.

Part 1 Planning Your Donation Request
1. Compile a list of donors. Before you begin asking for money, it's best to have an idea of who you're going to ask for donations. If you're going door-to-door, that may be as simple as deciding which neighborhood(s) to work in. If you're soliciting donations by phone or by mail, though, you'll need a list of prospective donors to contact.
If you can identify past donors on your list of people to call or write to, you may want to prioritize those individuals as "best bets" - these are people who, given their history of donating in the past, will most likely contribute again to your cause.
Try to identify which people on your list are the most financially stable. You can do this by interacting with the individual to get a sense of his or her finances, or if going door-to-door, look at the houses residents live in and the cars in their driveways. People with large, elaborate homes or flashy sports cars most likely have more disposable income. (Though of course this doesn't guarantee that they will give donations.)
You can also look for potential donors by their other areas of spending. For example, does the prospective donor attend fundraisers for other organizations or individuals? If so, that prospective donor probably has the means to donate to your organization, if properly persuaded.
Consider using analytical software and services, such as Donor Search, to identify which potential donors are more wealthy and more likely to donate.
Remember to think "ABC" when identifying donors: Able to make a gift, Belief (known or potential) in your cause, and Contact/Connection with your organization.
2. Get to know your donors. If your organization has dealt with donors in the past, you or a colleague will probably know what strategies work best in making your appeal. Some people want to know how the money from last year was spent, while others may simply want to know how much is needed. Certain donors may have fears or reservations about donating, and it's important to learn to recognize those fears/reservations so you can address them in advance.
Some donors may need to hear particular terms or phrases in order to be persuaded to donate. If you know this to be the case, make some indication of this on your list so that when you call or approach that person, you'll know what to say.
Any time a donor seems reluctant to give but gives anyway, make a note of that situation on your list or in that donor's file (if you have one). Listen to what the individual says when he or she is reluctant, and try to find ways to assuage those fears - not just for this year's fundraiser, but for future years as well.
Be aware that many well-known philanthropists hire other individuals to manage donations and contributions. Because of this, you may not get to speak to the actual donor himself/herself. However, the employees hired by a philanthropist probably have the same concerns that the philanthropist does, and you may have some luck appealing to the philanthropist's interests through his or her employees.
3. Find ways to present your organization. People who have donated to your organization will no doubt be familiar with who you are (as an organization) and what you do. But what about people who have never donated before? How will you describe what you do to an outsider? This is important, as it may determine whether the individual will listen to the rest of your pitch. If possible, try to compile some data on what your organization has done in the past, the problems you hope to address after this fundraising drive, and how that prospective donation would help your cause.
Try to present your organization in a way that both explains what you do while also highlighting the issue you seek to change. For example, you might say something like, "Did you know that [the issue your organization addresses] affects a significant portion of the city, and we are the only organization solely committed to addressing these issues in a comprehensive way?"
It's not a requirement to have data compiled, but for individuals who aren't familiar with your organization, it may be very helpful to know that information.
Consider printing out a brochure or having a reusable chart to illustrate both the improvements you've made and the improvements you hope to make.
Think about what you might say if someone doesn't understand your organization's goals, or what you might say if someone was dismissive of your organization. Try putting yourself in those shoes - imagining that you were someone who didn't want to help the organization - and what you might say to the organization. Then imagine how you might respond to hearing those words.
The better your donor base understands your organization - and the better you understand your donors - the more likely you'll be to build a long-term relationship with that donor.
4. Practice your appeal. One of the best things you can do to strengthen your appeal for donations is to practice what you're going to say. That doesn't just mean knowing how to actually ask for money, but also knowing how to initiate the conversation, practicing scenarios, anticipating potential responses, and knowing how to direct (or re-direct) the conversation.
Remember that the best appeal will educate the potential donor, rather than making a simple sales pitch.
Practice your appeal out loud. Get comfortable with the speech, and learn to adapt it to your own style of speaking. Make it your own speech, and try to make it feel comfortable and unrehearsed (even though this may take a lot of rehearsal).
Practice in front of a mirror if you will be interacting with donors face-to-face.
Try recording yourself, either with a tape recorder or on video, and study your mannerisms and your speech patterns. Does it sound honest? Do your vocal patterns and your physical mannerisms communicate the message of your organization, and the urgency of what you're trying to solve?

Part 2 Asking for Donations.
1. Start a conversation. Don't just call and start running in with your pitch. Work on creating a dialogue with the potential donor, which may mean making some polite small talk at the start. It can be as simple as asking the person how his or her day is going. Anything to start a conversation should help disarm the individual, and make the person realize that you're a caring and concerned member of the community.
If the prospective donor is a known philanthropist, he or she may prefer to have someone who heads the foundation ask for a donation. Statistically, donors are more likely to give money to a recognizable figure affiliated with an organization, rather than to a fundraiser who contacts them on the organization's behalf.
Initiate the conversation by getting the prospective donor to acknowledge an existing problem. If you're raising money for a local organization, you might open the conversation by asking what he or she thinks is the greatest crisis facing your region.
2. Make your intentions known. You shouldn't just introduce yourself by asking for money, but you should make your intentions known near the end of your small talk. Start by asking how the person is doing, or commenting on the weather, and then use that as a lead-in to say, "I'm working with _______, and we're trying to help _______ be able to ________."
If the individual feels like you're just having an aimless conversation and then suddenly he or she is asked for money, it may create tension and cause the person to feel like you're shaking them down. Be calm, friendly, and casual, but don't drag your feet about making it clear that you have a purpose.
3. Let the other person speak. Chances are, if you launch into your usual appeal to a person on the street who's never donated before, that person will walk away. But if you have created a dialogue, and made room for the other person to speak, you may be able to get that individual to feel engaged and a part of the solution.
Try asking a Question : . Say something like, "What do you think is the biggest problem our community faces?" Once the person has answered, instead of simply saying, "Yes, you're right. Will you consider donating?" try a more nuanced approach. After the person says what he or she sees as the problem, just say, "How interesting!" and keep silent while remaining interested.
People fear silence, and the person will probably fill that gap by elaborating on why that issue is important. That potential donor may go on to talk about how a family member has been affected by those issues. This gives you an in to take the specific concern he/she has and run with it. It's no longer an abstract concern, but a specific problem that may have affected the individual personally.
4. Make a specific request. If you leave a donation appeal open-ended, the person may not end up donating, or may only give a few dollars. But if you ask for a specific amount, it takes a lot of guess work out of the equation for that individual, and makes it easier to commit to your request. For example, if the person seems interested, say something like, "Well, we can make a difference. For just _____ dollars, you can help accomplish ___________."
Another way to ask for a specific amount is to put the ball in their court. Ask something like, "Would you consider a gift of _____?" or "Is ______ something you'd be willing to consider to help tackle the problem of __________?"
5. Be persistent. Many people will say no right off the bat, but others may simply need to be persuaded a bit more. Perhaps someone might say that the amount you requested is too high. If that happens, let the person know that any donation amount would be a big help, and ask if there's a slightly lower amount that the person would be willing/able to donate.
Don't be aggressive with your appeal, but do be insistent that your cause is worthy and that any donation amount would help that cause.
6. Thank the person either way. If the individual is willing to donate, then it's cause for celebration. You can thank the person and let him or her know that that donation will go a long way towards solving or addressing the issue at hand. But even if the person is not interested in donating, you should still be polite and appreciative of their time. Simply say, "Well, thank you for your time and have a wonderful day."
Expressing gratitude and courtesy can go a long way. Just because someone isn't interested in donating, that doesn't mean the situation won't change. Perhaps next year the people who said no will have heard or read more about your organization, or perhaps the individual will have been personally affected by the issue you're seeking to address. Making a good impression now, even when turned down, may be what helps you get a donation next year.
7. Follow up with donors. If someone gave a donation, you should absolutely express gratitude. Send the donor a thank-you letter and a gift receipt (in case they want to write it off on their taxes or simply have a record of the donation). It's best to send these items as quickly as possible so that the donor knows that the contribution was greatly appreciated and will be put to good use.

Community Q&A.

Question : How do I ask a rich person for 50,000 dollars?
Answer : Follow the instructions listed in the article above. However, they will likely say no.
Question : How can I get money if I need it urgently?
Answer : Get a job, start a blog, make something, or ask for a small loan.
Question : How can I get help with my power bills and the foreclosure on my house?
Answer : There are probably social services nearby that can help.
Question : How can I raise money for my wedding?
Answer : Ask friends and family members if they are willing to pitch in some money to help fund your marriage. In return, send them invitations.
Question : How can I find money for my daughter's marriage?
Answer : Loans, relatives, friends, or you could try planning a wedding that won't cost you much!
Question : Where can you apply for a small business loan with bad credit?
Answer : You can try becoming a member of a credit union and try for a loan there.
Question : How do I ask for money if I am about to be homeless with an autistic son?
Answer : Ask family and friends, and tell them your situation. Look for government programs that can help, and depending on the age of your son, you may be able to get financial help for him. You can also ask family and friends if the two of you can stay with them while you get back on your feet. That way, you have an address while you look for a job.
Question : I need a loan to deal with a parent's sickness, what can I do?
Answer : Loans are not the only solution to sickness, there are organizations that provide affordable medical care. Search for these in your area. You might also consider launching a donation campaign through Kickstarter or another fundraising website.
Question : How can someone fund me to help me spread the word of God?
Answer : Try doing a simple fundraiser, like a lemonade stand or a car wash.

Tips.

Many people are more motivated to help you with money if they sympathize with your goals or interests. Try to tailor your appeal to each individual donor, based on how that donor seems to respond to the issues you address.
Always send a thank-you note to your donors, regardless of how much they sent you.

July 02, 2020

How did Warren Buffett get started in business?

How did Warren Buffett get started in business?

By BRENT RADCLIFFE.
Warren Buffett may have been born with business in his blood. He purchased his first stock when he was 11 years old and worked in his family’s grocery store in Omaha.
His father, Howard Buffett, owned a small brokerage, and Warren would spend his days watching what investors were doing and listening to what they said. As a teenager, he took odd jobs, from washing cars to delivering newspapers, using his savings to purchase several pinball machines that he placed in local businesses.

His entrepreneurial successes as a youth did not immediately translate into a desire to attend college. His father pressed him to continue his education, with Buffett reluctantly agreeing to attend the University of Pennsylvania. He then transferred to the University of Nebraska, where he graduated with a degree in business in three years.

After being rejected by the Harvard Business School, he enrolled in graduate studies at Columbia Business School. While there, he studied under Benjamin Graham – who became a lifelong friend – and David Dodd, both well-known securities analysts. It was through Graham's class in securities analysis that Buffett learned the fundamentals of value investing. He once stated in an interview that Graham's book, The Intelligent Investor, had changed his life and set him on the path of professional analysis to the investment markets. Along with Security Analysis, co-written by Graham and Dodd it provided him the proper intellectual framework and a road map for investing.

Benjamin Graham and The Intelligent Investor.
Graham is often called the "Dean of Wall Street" and the father of value investing, as one of the most important early proponents of financial security analysis. He championed the idea that the investor should look at the market as though it were an actual entity and potential business partner – Graham called this entity "Mr. Market" – that sometimes asks for too much or too little money to be bought out.

It would be difficult to summarize all of Graham's theories in full. At its core, value investing is about identifying stocks that have been undervalued by the majority of stock market participants. He believed that stock prices were frequently wrong due to irrational and excessive price fluctuations (both upside and downside). Intelligent investors, said Graham, need to be firm in their principles and not follow the crowd.
Graham wrote The Intelligent Investor in 1949 as a guide for the common investor. The book championed the idea of buying low-risk securities in a highly diversified, mathematical way. Graham favored fundamental analysis, capitalizing on the difference between a stock's purchase price and its intrinsic value.

Entering the Investment Field.
Before working for Benjamin Graham, Warren had been an investment salesman – a job that he liked doing, except when the stocks he suggested dropped in value and lost money for his clients. To minimize the potential of having irate clients, Warren started a partnership with his close friends and family. The partnership had unique restrictions attached to it. Warren himself would invest only $100 and, through re-invested management fees, would grow his stake in the partnership. Warren would take half of the partnership’s gains over 4% and would repay the partnership a quarter of any loss incurred. Furthermore, money could only be added or withdrawn from the partnership on December 31st, and partners would have no input about the investments in the partnership.

By 1959, Warren had opened a total of seven partnerships and had a 9.5% stake in more than a million dollars of partnership assets. Three years later by the time he was 30, Warren was a millionaire and merged all of his partnerships into a single entity.
It was at this point that Buffett’s sights turned to directly investing in businesses. He made a $1 million investment in a windmill manufacturing company, and the next year in a bottling company. Buffett used the value-investing techniques he learned in school, as well as his knack for understanding the general business environment, to find bargains on the stock market.

Buying Berkshire Hathaway.
In 1962, Warren saw an opportunity to invest in a New England textile company called Berkshire Hathaway and bought some of its stock. Warren began to aggressively buy shares after a dispute with its management convinced him that the company needed a change in leadership..  Ironically, the purchase of Berkshire Hathaway is one of Warren’s major regrets.
Understanding the beauty of owning insurance companies – clients pay premiums today to possibly receive payments decades later – Warren used Berkshire Hathaway as a holding company to buy National Indemnity Company (the first of many insurance companies he would buy) and used its substantial cash flow to finance further acquisitions.

As a value investor, Warren is a sort of jack-of-all-trades when it comes to industry knowledge. Berkshire Hathaway is a great example. Buffett saw a company that was cheap and bought it, regardless of the fact that he wasn’t an expert in textile manufacturing. Gradually, Buffett shifted Berkshire’s focus away from its traditional endeavors, instead using it as a holding company to invest in other businesses. Over the decades, Warren has bought, held and sold companies in a variety of different industries.

Some of Berkshire Hathaway’s most well-known subsidiaries include, but are not limited to, GEICO (yes, that little Gecko belongs to Warren Buffett), Dairy Queen, NetJets, Benjamin Moore & Co., and Fruit of the Loom.  Again, these are only a handful of companies of which Berkshire Hathaway has a majority share.
The company also has interests in many other companies, including American Express Co. (AXP), Costco Wholesale Corp. (COST), DirectTV (DTV), General Electric Co. (GE), General Motors Co. (GM), Coca-Cola Co. (KO), International Business Machines Corp. (IBM), Wal-Mart Stores Inc. (WMT), Proctor & Gamble Co. (PG) and Wells Fargo & Co. (WFC).

Berkshire Woes and Rewards.
Business for Buffett hasn’t always been rosy, though. In 1975, Buffett and his business partner, Charlie Munger, were investigated by the Securities and Exchange Commission (SEC) for fraud. The two maintained that they had done nothing wrong and that the purchase of Wesco Financial Corporation only looked suspicious because of their complex system of businesses.
Further trouble came with a large investment in Salomon Inc. In 1991, news broke of a trader breaking Treasury bidding rules on multiple occasions, and only through intense negotiations with the Treasury did Buffett manage to stave off a ban on buying Treasury notes and subsequent bankruptcy for the firm.
In more recent years, Buffett has acted as a financier and facilitator of major transactions. During the Great Recession, Warren invested and lent money to companies that were facing financial disaster. Roughly 10 years later, the effects of these transactions are surfacing and they’re enormous.

A loan to Mars Inc. resulted in a $680 million profit.
Wells Fargo & Co. (WFC), of which Berkshire Hathaway bought almost 120 million shares during the Great Recession, is up more than 7 times from its 2009.
American Express Co. (AXP) is up about five times since Warren’s investment in 200813
Bank of America Corp. (BAC) pays $300 million a year and Berkshire Hathaway has the option to buy additional shares at around $7 each – less than half of what it trades at today.
Goldman Sachs Group Inc. (GS) paid out $500 million in dividends a year and a $500 million redemption bonus when they repurchased the shares.

Most recently, Warren has partnered up with 3G Capital to merge J.H. Heinz Company and Kraft Foods to create the Kraft Heinz Food Company (KHC). The new company is the third largest food and beverage company in North America and fifth largest in the world, and boasts annual revenues of $28 billion. In 2017, he bought up a significant stake in Pilot Travel Centers, the owners of the Pilot Flying J chain of truck stops. He will become a majority owner over a six-year period.
Modesty and quiet living meant that it took Forbes some time to notice Warren and add him to the list of richest Americans, but when they finally did in 1985, he was already a billionaire. Early investors in Berkshire Hathaway could have bought in as low as $275 a share and by 2014 the stock price had reached $200,000, and was trading just under $300,000 earlier this year.

Comparing Buffett to Graham.
Buffett has referred to himself as "85% Graham." Like his mentor, he has focused on company fundamentals and a "stay the course" approach – an approach that enabled both men to build huge personal nest eggs. Seeking a seeks a strong return on investment (ROI), Buffett typically looks for stocks that are valued accurately and offer robust returns for investors.
However, Buffett invests using a more qualitative and concentrated approach than Graham did. Graham preferred to find undervalued, average companies and diversify his holdings among them; Buffett favors quality businesses that already have reasonable valuations (though their stock should still be worth something more) and the ability for large growth.

Other differences lie in how to set intrinsic value, when to take a chance and how deeply to dive into a company that has potential. Graham relied on quantitative methods to a far greater extent than Buffett, who spends his time actually visiting companies, talking with management and understanding the corporate's particular business model. As a result, Graham was more able to and more comfortable investing in lots of smaller companies than Buffett. Consider a baseball analogy: Graham was concerned about swinging at good pitches and getting on base; Buffett prefers to wait for pitches that allow him to score a home run. Many have credited Buffett with having a natural gift for timing that cannot be replicated, whereas Graham's method is friendlier to the average investor.

Buffett Fun Facts.
Buffett only began making large-scale charitable donations at age 75.
Buffett has made some interesting observations about income taxes. Specifically, he's questioned why his effective capital gains tax rate of around 20% is a lower income tax rate than that of his secretary – or for that matter, than that paid by most middle-class hourly or salaried workers. As one of the two or three richest men in the world, having long ago established a mass of wealth that virtually no amount of future taxation can seriously dent, Mr. Buffett offers his opinion from a state of relative financial security that is pretty much without parallel. Even if, for example, every future dollar Warren Buffett earns is taxed at the rate of 99%, it is doubtful that it would affect his standard of living.

Buffett has described The Intelligent Investor as the best book on investing that he has ever read, with Security Analysis a close second. Other favorite reading matter includes:
Common Stocks and Uncommon Profits by Philip A. Fisher, which advises potential investors to not only examine a company's financial statements but to evaluate its management. Fisher focuses on investing in innovative companies, and Buffett has long held him in high regard.
The Outsiders by William N. Thorndike profiles eight CEOs and their blueprints for success. Among the profiled is Thomas Murphy, friend to Warren Buffett and director for Berkshire Hathaway. Buffett has praised Murphy, calling him "overall the best business manager I've ever met."
Stress Test by former Secretary of the Treasury, Timothy F. Geithner, chronicles the financial crisis of 2008-9 from a gritty, first-person perspective. Buffett has called it a must-read for managers, a textbook for how to stay level under unimaginable pressure.
Business Adventures: Twelve Classic Tales from the World of Wall Street by John Brooks is a collection of articles published in The New Yorker in the 1960s. Each tackles famous failures in the business world, depicting them as cautionary tales. Buffett lent his copy of it to Bill Gates, who reportedly has yet to return it.

The Bottom Line.
Warren Buffett’s investments haven't always been successful, but they were well-thought-out and followed value principles. By keeping an eye out for new opportunities and sticking to a consistent strategy, Buffett and the textile company he acquired long ago are considered by many to be one of the most successful investing stories of all time. But you don't have to be a genius "to invest successfully over a lifetime," the man himself claims. "What's needed is a sound intellectual framework for making decisions and the ability to keep emotions from corroding that framework."

August 04, 2020

How to Use the Rule of 72

How to Use the Rule of 72.

The Rule of 72 is a handy tool used in finance to estimate the number of years it would take to double a sum of money through interest payments, given a particular interest rate. The rule can also estimate the annual interest rate required to double a sum of money in a specified number of years. The rule states that the interest rate multiplied by the time period required to double an amount of money is approximately equal to 72.
The Rule of 72 is applicable in cases of exponential growth, (as in compound interest) or in exponential "decay," as in the loss of purchasing power caused by monetary inflation.

Method 1 Estimating "Doubling" Time.
1. Let R x T = 72. R is the rate of growth (the annual interest rate), and T is the time (in years) it takes for the amount of money to double.
2. Insert a value for R. For example, how long does it take to turn $100 into $200 at a yearly interest rate of 5%? Letting R = 5, we get 5 x T = 72.
3. Solve for the unknown variable. In this example, divide both sides of the above equation by R (that is, 5) to get T = 72 ÷ 5 = 14.4. So it takes 14.4 years for $100 to double at an interest rate of 5% per annum. (The initial amount of money doesn't matter. It will take the same amount of time to double no matter what the beginning amount is.)
4. Study these additional examples:
How long does it take to double an amount of money at a rate of 10% per annum? 10 x T = 72. Divide both sides of the equation by 10, so that T = 7.2 years.
How long does it take to turn $100 into $1600 at a rate of 7.2% per annum? Recognize that 100 must double four times to reach 1600 ($100 → $200, $200 → $400, $400 → $800, $800 → $1600). For each doubling, 7.2 x T = 72, so T = 10. So, as each doubling takes ten years, the total time required (to change $100 into $1,600) is 40 years.

Method 2 Estimating the Growth Rate.
1. Let R x T = 72. R is the rate of growth (the interest rate), and T is the time (in years) it takes to double any amount of money.
2. Enter the value of T. For example, let's say you want to double your money in ten years. What interest rate would you need in order to do that? Enter 10 for T in the equation. R x 10 = 72.
3. Solve for R. Divide both sides by 10 to get R = 72 ÷ 10 = 7.2. So you will need an annual interest rate of 7.2% in order to double your money in ten years.

Method 3 Estimating Exponential "Decay" (Loss).
1. Estimate the time it would take to lose half of your money (or its purchasing power in the wake of inflation). Let T = 72 ÷ R. This is the same equation as above, just slightly rearranged. Now enter a value for R. An example.
How long will it take for $100 to assume the purchasing power of $50, given an inflation rate of 5% per year?
Let 5 x T = 72, so that T = 72 ÷ 5 = 14.4. That's how many years it would take for money to lose half its buying power in a period of 5% inflation. (If the inflation rate were to change from year to year, you would have to use the average inflation rate that existed over the full time period.)
2. Estimate the rate of decay (R) over a given time span: R = 72 ÷ T. Enter a value for T, and solve for R. For example.
If the buying power of $100 becomes $50 in ten years, what is the inflation rate during that time?
R x 10 = 72, where T = 10. Then R = 72 ÷ 10 = 7.2%.
3. Ignore any unusual data. If you can detect a general trend, don't worry about temporary numbers that are wildly out of range. Drop them from consideration.

Method 4 Derivation.
1. Understand how the derivation works for periodic compounding.
For periodic compounding, FV = PV (1 + r)^T, where FV = future value, PV = present value, r = growth rate, T = time.
If money has doubled, FV = 2*PV, so 2PV = PV (1 + r)^T, or 2 = (1 + r)^T, assuming the present value is not zero.
Solve for T by taking the natural logs on both sides, and rearranging, to get T = ln(2) / ln(1 + r).
The Taylor series for ln(1 + r) around 0 is r - r2/2 + r3/3 - ... For low values of r, the contributions from the higher power terms are small, and the expression approximates r, so that t = ln(2) / r.
Note that ln(2) ~ 0.693, so that T ~ 0.693 / r (or T = 69.3 / R, expressing the interest rate as a percentage R from 0-100%), which is the rule of 69.3. Other numbers such as 69, 70, and 72 are used for easier calculations.
2. Understand how the derivation works for continuous compounding. For periodic compounding with multiple compounding per year, the future value is given by FV = PV (1 + r/n)^nT, where FV = future value, PV = present value, r = growth rate, T = time, and n = number of compounding periods per year. For continuous compounding, n approaches infinity. Using the definition of e = lim (1 + 1/n)^n as n approaches infinity, the expression becomes FV = PV e^(rT).
If money has doubled, FV = 2*PV, so 2PV = PV e^(rT), or 2 = e^(rT), assuming the present value is not zero.
Solve for T by taking natural logs on both sides, and rearranging, to get T = ln(2)/r = 69.3/R (where R = 100r to express the growth rate as a percentage). This is the rule of 69.3.
For continuous compounding, 69.3 (or approximately 69) gives more accurate results, since ln(2) is approximately 69.3%, and R * T = ln(2), where R = growth (or decay) rate, T = the doubling (or halving) time, and ln(2) is the natural log of 2. 70 may also be used as an approximation for continuous or daily (which is close to continuous) compounding, for ease of calculation. These variations are known as rule of 69.3, rule of 69, or rule of 70.
A similar accuracy adjustment for the rule of 69.3 is used for high rates with daily compounding: T = (69.3 + R/3) / R.
The Eckart-McHale second order rule, or E-M rule, gives a multiplicative correction to the Rule of 69.3 or 70 (but not 72), for better accuracy for higher interest rate ranges. To compute the E-M approximation, multiply the Rule of 69.3 (or 70) result by 200/(200-R), i.e., T = (69.3/R) * (200/(200-R)). For example, if the interest rate is 18%, the Rule of 69.3 says t = 3.85 years. The E-M Rule multiplies this by 200/(200-18), giving a doubling time of 4.23 years, which better approximates the actual doubling time 4.19 years at this rate.
The third-order Padé approximant gives even better approximation, using the correction factor (600 + 4R) / (600 + R), i.e., T = (69.3/R) * ((600 + 4R) / (600 + R)). If the interest rate is 18%, the third-order Padé approximant gives T = 4.19 years.
To estimate doubling time for higher rates, adjust 72 by adding 1 for every 3 percentages greater than 8%. That is, T = [72 + (R - 8%)/3] / R. For example, if the interest rate is 32%, the time it takes to double a given amount of money is T = [72 + (32 - 8)/3] / 32 = 2.5 years. Note that 80 is used here instead of 72, which would have given 2.25 years for the doubling time.


FAQ.
Question : When would I need to use the rule of 72?
Answer : It's a handy shortcut when considering compounded, monetary gains or losses. For example, you might want to know how long it would take for invested money to double in value, given a specific rate of interest.
Question : How do I calculate compound interest?
Answer : The formula for annual compound interest (A) is: P [1 + (r / n)]^(nt), where P=principal amount, r = the annual interest rate as a decimal, n = the number of times the interest is compounded per year, and t = the number of years of the loan or investment.
Question : What is APY for an APR of 3.5% compounded?
Answer : It depends on how often the interest compounds: annually, semi-annually, quarterly, monthly or daily.

Tips.

Let the Rule of 72 work for you by starting to save now. At a growth rate of 8% a year (the approximate rate of return in the stock market), you would double your money in nine years (72 ÷ 8 = 9), quadruple your money in 18 years, and have 16 times your money in 36 years.
The value of 72 was chosen as a convenient numerator in the above equation. 72 is easily divisible by several small numbers: 1,2,3,4,6,8,9, and 12. It provides a good approximation for annual compounding at typical rates (from 6% to 10%). The approximations are less exact at higher interest rates.
You can use Felix's Corollary to the Rule of 72 to calculate the "future value" of an annuity (that is, what the annuity's face value will be at a specified future time). You can read about the corollary on various financial and investing websites.

Warnings.
Let the rule of 72 convince you not to take on high-interest debt (as is typical with credit cards). At an average interest rate of 18%, semiretired credit card debt doubles in just four years (72 ÷ 18 = 4), quadruples in eight years, and becomes completely unmanageable after that.

April 10, 2020