The Rule of 72: What It Is and How to Use It in Investing (2024)

Rate of ReturnRule of 72Actual # of YearsDifference (#) of Years
2%36.0351.0
3%24.023.450.6
5%14.414.210.2
7%10.310.240.0
9%8.08.040.0
12%6.06.120.1
25%2.93.110.2
50%1.41.710.3
72%1.01.280.3
100%0.710.3

Notice that although it gives an estimate, the Rule of 72 is less precise as rates of return increase.

1:10

Rule Of 72

The Rule of 72 and Natural Logs

The Rule of 72 can estimate compounding periods using natural logarithms. In mathematics, the logarithm is the opposite concept of a power; for example, the opposite of 10³ is log base 10 of 1,000.

Ruleof72=ln(e)=1where:e=2.718281828\begin{aligned} &\text{Rule of 72} = ln(e) = 1\\ &\textbf{where:}\\ &e = 2.718281828\\ \end{aligned}Ruleof72=ln(e)=1where:e=2.718281828

e is a famous irrational number similar to pi. The mostimportantproperty of the numbereis related to the slope of exponential and logarithm functions, and it's first few digits are 2.718281828.

The natural logarithm is the amount of time needed to reach a certain level of growth withcontinuous compounding.

The time value of money (TVM) formula is the following:

FutureValue=PV×(1+r)nwhere:PV=PresentValuer=InterestRaten=NumberofTimePeriods\begin{aligned} &\text{Future Value} = PV \times (1+r)^n\\ &\textbf{where:}\\ &PV = \text{Present Value}\\ &r = \text{Interest Rate}\\ &n = \text{Number of Time Periods}\\ \end{aligned}FutureValue=PV×(1+r)nwhere:PV=PresentValuer=InterestRaten=NumberofTimePeriods

To see how long it will take an investment to double, state the future value as 2 and the present value as 1.

2=1×(1+r)n2 = 1 \times (1 + r)^n2=1×(1+r)n

Simplify, and you have the following:

2=(1+r)n2 = (1 + r)^n2=(1+r)n

To remove the exponent on the right-hand side of the equation, take the natural log of each side:

ln(2)=n×ln(1+r)ln(2) = n \times ln(1 + r)ln(2)=n×ln(1+r)

This equation can be simplified again because the natural log of (1 + interest rate) equals the interest rate as the rate getscontinuously closerto zero. In other words, you are left with:

ln(2)=r×nln(2) = r \times nln(2)=r×n

The natural log of 2 is equal to 0.693 and, after dividing both sides by the interest rate, you have:

0.693/r=n0.693/r = n0.693/r=n

By multiplying the numerator and denominator on the left-hand side by 100, you can express each as a percentage. This gives:

69.3/r%=n69.3/r\% = n69.3/r%=n

How to Adjust the Rule of 72 for Higher Accuracy

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.

Many investors prefer to use the Rule of 69.3 rather than the Rule of 72. For maximum accuracy—particularly forcontinuous compounding interest rateinstruments—use the Rule of 69.3.

The number 72 has many convenient factors including two, three, four, six, and nine. This convenience makes it easier to use the Rule of 72 for a close approximation of compounding periods.

How toCalculate the Rule of 72 Using Matlab

The calculation of the Rule of 72 in Matlab requires running a simple command of "years = 72/return," where the variable "return" is the rate of return on investment and "years" is the result for the Rule of 72. The Rule of 72 is also used to determine how long it takes for money to halve in value for a given rate ofinflation. For example, if the rate of inflation is 4%, a command "years = 72/inflation" where the variable inflation is defined as "inflation = 4" gives 18 years.

The Rule of 72: What It Is and How to Use It in Investing (2024)

FAQs

The Rule of 72: What It Is and How to Use It in Investing? ›

Do you know the Rule of 72? It's an easy way to calculate just how long it's going to take for your money to double. Just take the number 72 and divide it by the interest rate you hope to earn. That number gives you the approximate number of years it will take for your investment to double.

Does the Rule of 72 work for stocks? ›

The Rule of 72 is reasonably accurate for low rates of return. The chart below compares the numbers given by the Rule of 72 and the actual number of years it takes an investment to double. Notice that although it gives an estimate, the Rule of 72 is less precise as rates of return increase.

What are 3 things that the Rule of 72 can determine? ›

What Are Three Things The Rule Of 72 Can Determine?
  • Given a fixed annual rate of return, how long will it take for an investment to double.
  • The approximate number of years it will take for an investment to double.
  • That compounding can significantly impact the length of time it takes for an investment to double.

How much interest does $10000 earn in a year? ›

Currently, money market funds pay between 4.47% and 4.87% in interest. With that, you can earn between $447 to $487 in interest on $10,000 each year.

How long will it take to double this investment using the Rule of 72? ›

The rule says that to find the number of years required to double your money at a given interest rate, you just divide the interest rate into 72. For example, if you want to know how long it will take to double your money at eight percent interest, divide 8 into 72 and get 9 years.

How many years will it take $100 to double in value at an annual interest rate of 10 percent? ›

Rate =10% FV =200 PV =100 FV=PV*(1+r)^n 200=100*(1+10%)^n applying log on both sides n=log(2)/log(1.10) =7.3 years (Option d is correct option) … Transcribed image text: O At an annual interest rate of 10 percent, about how many years will it take $100 to double in value?

What is the 80% Rule in stock market? ›

Based on the application of famed economist Vilfredo Pareto's 80-20 rule, here are a few examples: 80% of your stock market portfolio's profits might come from 20% of your holdings. 80% of a company's revenues may derive from 20% of its clients.

What is the Rule of 72 for dummies? ›

What is the Rule of 72? The Rule of 72 is a calculation that estimates the number of years it takes to double your money at a specified rate of return. If, for example, your account earns 4 percent, divide 72 by 4 to get the number of years it will take for your money to double. In this case, 18 years.

How can I double my money without risk? ›

5 Ways to Double Your Money
  1. Take Advantage of 401(k) Matching.
  2. Invest in Value and Growth Stocks.
  3. Increase Your Contributions.
  4. Consider Alternative Investments.
  5. Be Patient.
Nov 1, 2022

What is the rule of 42 in investing? ›

The so-called Rule of 42 is one example of a philosophy that focuses on a large distribution of holdings, calling for a portfolio to include at least 42 choices while owning only a small amount of most of those choices.

Can I live off the interest of $100000? ›

Interest on $100,000

Even with a well-diversified portfolio and minimal living expenses, this amount is not high enough to provide for most people. Investing this amount in a low-risk investment like a savings account with a rate between 2% to 2.50% of interest each year would return $2,000 to $2,500.

How much interest on $1 million dollars per year? ›

Bank Savings Accounts

As noted above, the average rate on savings accounts as of February 3rd 2021, is 0.05% APY. A million-dollar deposit with that APY would generate $500 of interest after one year ($1,000,000 X 0.0005 = $500).

Can you live off 10 million dollars interest? ›

It's entirely possible to live off the interest earned by a $10 million portfolio, depending on how much you need and what your investment choices are. You'll want to make sure that your lifestyle goals are in line with the income produced if you're going to make it through retirement without running out of funds.

How to make 10 percent on your money? ›

Where can I get 10 percent return on investment?
  1. Invest in stock for the long haul. ...
  2. Invest in stocks for the short term. ...
  3. Real estate. ...
  4. Investing in fine art. ...
  5. Starting your own business. ...
  6. Investing in wine. ...
  7. Peer-to-peer lending. ...
  8. Invest in REITs.

How much interest does $20000 earn in a year? ›

How much $20,000 earns you in a savings account
APYInterest earned in one year
0.35%$70
3.50%$700
4.00%$800
4.50%$900
3 more rows
Mar 20, 2023

What is the rule of 69? ›

What is Rule of 69. Rule of 69 is a general rule to estimate the time that is required to make the investment to be doubled, keeping the interest rate as a continuous compounding interest rate, i.e., the interest rate is compounding every moment.

How much is $100 a week for 10 years? ›

This is even more surprising: If Annie can keep finding that extra $100 per week for another 10 years, she'll be sitting on roughly $2 million at the end of that 40-year stretch. Those are jaw-dropping numbers, to be sure. But the math has been checked. It's right!

What is 5% interest on $5000? ›

If you have $5,000 in a savings account that pays five percent interest, you will earn $250 in interest each year.

How much is $1000 worth at the end of 2 years if the interest rate of 6% is compounded daily? ›

Hence, if a two-year savings account containing $1,000 pays a 6% interest rate compounded daily, it will grow to $1,127.49 at the end of two years.

What is the number 1 rule of stocks? ›

1 – Never lose money. Let's kick it off with some timeless advice from legendary investor Warren Buffett, who said “Rule No. 1 is never lose money.

What is the golden rule of investing in stocks? ›

Warren Buffet's first rule of investing is to never lose money; his second is to never forget the first rule. This golden rule is key for long-term capital protection and growth.

What is 15 15 15 rule stock market? ›

The 15-15-15 rule is concentrated on investing in values of 15s. As per the 15-15-15 rule, mutual funds investors invest in ₹15000 SIP per month at a rate of interest of 15% for 15 years. And at the end of tenure, likely to generate approximately ₹1 crore.

What are two examples of how the Rule of 72 can be used? ›

You can also use the rule of 72 for expenses like inflation or interest: If inflation rates go from 2% to 3%, your money will lose half its value in 24 years instead of 36. If college tuition increases at 5% per year (which is faster than inflation), tuition costs will double in 72/5 or about 14.4 years.

What are two uses for the Rule of 72? ›

The Rule of 72 can be applied to anything that increases exponentially, such as GDP or inflation; it can also indicate the long-term effect of annual fees on an investment's growth. This estimation tool can also be used to estimate the rate of return needed for an investment to double given an investment period.

What is the 50 30 20 rule? ›

One of the most common types of percentage-based budgets is the 50/30/20 rule. The idea is to divide your income into three categories, spending 50% on needs, 30% on wants, and 20% on savings. Learn more about the 50/30/20 budget rule and if it's right for you.

How to invest $1,000 dollars and double it? ›

How to Invest $1000: 7 Smart Ways to Grow $1K in 2023
  1. Deal with debt.
  2. Invest in Low-Cost ETFs.
  3. Invest in stocks with fractional shares.
  4. Build a portfolio with a robo-advisor.
  5. Contribute to a 401(k)
  6. Contribute to a Roth IRA.
  7. Invest in your future self.
Jan 29, 2023

What is the safest investment with highest return? ›

High-quality bonds and fixed-indexed annuities are often considered the safest investments with the highest returns. However, there are many different types of bond funds and annuities, each with risks and rewards. For example, government bonds are generally more stable than corporate bonds based on past performance.

How to invest $5,000 dollars for quick return? ›

How to Invest $5,000
  1. Try real estate investing for rental income.
  2. Invest in individual stocks.
  3. Invest in mutual funds or ETFs.
  4. Consider low-risk bonds.
  5. Leverage robo-advisors for hands-off investing.
  6. Open a CD for steady returns.
  7. Put a little into cryptocurrency for high potential returns.
Mar 29, 2023

What is the 3 6 9 rule investing? ›

Those general saving targets are often called the “3-6-9 rule”: savings of 3, 6, or 9 months of take-home pay. Here are some guidelines to help you decide what total savings fits your needs.

What is Rule 25 in investing? ›

The Rule of 25 is a potentially useful way for you to get a sense of how much money you will need to save to have a financially secure retirement. The rule states that if you save 25 times of what you want your annual salary to be in retirement, that you can stretch that money for 30 years.

How much does the average 70 year old have in savings? ›

How much does the average 70-year-old have in savings? Just shy of $500,000, according to the Federal Reserve. The better question, however, may be whether that's enough for a 70-year-old to live on in retirement so that you can align your budget accordingly.

Can I retire at 55 with $2 million? ›

Yes, $2 million should be enough to retire. Annuities provide an income option to pay a guaranteed monthly amount for two lives.

Can I retire at 45 with $3 million dollars? ›

You can probably retire in financial comfort at age 45 if you have $3 million in savings. Although it's much younger than most people retire, that much money can likely generate adequate income for as long as you live.

Where do millionaires keep their money? ›

Millionaires have many different investment philosophies. These can include investing in real estate, stock, commodities and hedge funds, among other types of financial investments. Generally, many seek to mitigate risk and therefore prefer diversified investment portfolios.

How many people have $1000000 in savings? ›

In fact, statistically, around 10% of retirees have $1 million or more in savings.

How much interest does $3 million dollars earn per year? ›

A savings account at a bank or credit union pays from 0.01% to 1% per year. At those rates, $3 million would earn from $3,000 to $30,000 in interest per year.

Are you rich if you have 2 million dollars? ›

Being rich currently means having a net worth of about $2.2 million. However, this number fluctuates over time, and you can measure wealth according to your financial priorities. As a result, healthy financial habits, like spending less than you make, are critical to becoming wealthy, no matter your definition.

Am I rich if I have $10 million dollars? ›

You might need $5 million to $10 million to qualify as having a very high net worth while it may take $30 million or more to be considered ultra-high net worth. That's how financial advisors typically view wealth.

Can I retire on $500 K plus Social Security? ›

Yes, retiring at 55 with $500,000 is feasible. An annuity can offer a lifetime guaranteed income of $24,688 per year or an initial $21,000 that increases over time to offset inflation. At 62, Social Security Benefits augment this income. Both options continue payouts even if the annuity depletes.

Where is the safest place to put your retirement money? ›

Most of our experts agree that one of the safest places to keep your money is in a savings account insured by the Federal Deposit Insurance Corporation (FDIC). “High-yield savings accounts are an excellent option for those looking to keep their retirement savings safe.

What gives the highest return on investment? ›

A stock represents a share of ownership in a company. Stocks offer the biggest potential return on your investment while exposing your money to the highest level of volatility.

What is a good monthly return on investment? ›

According to many financial investors, 7% is an excellent return rate for most, while 5% is enough to be considered a 'good' return. Still, an investor may make more or less than the average percentage since everything depends on the investment's circ*mstances.

Can I live off interest on a million dollars? ›

Once you have $1 million in assets, you can look seriously at living entirely off the returns of a portfolio. After all, the S&P 500 alone averages 10% returns per year. Setting aside taxes and down-year investment portfolio management, a $1 million index fund could provide $100,000 annually.

How much interest will $300 000 earn a year? ›

Income After Retirement: Investments and Savings

The average retirement account generates an average return of about 5% annually. Some estimates place this number higher, but we'll use conservative math. With a retirement account of $300,000, this means an average return of about $15,000 per year.

How much interest does a million dollars make a year in a savings account? ›

High-Yield Savings: The average savings account interest rate, according to the FDIC, is just 0.24% — just $2,400 annually for a $1 million balance — but high-yield savings accounts offer rates around 3% to 4%, with a yield of $30,000 to $40,000 per year.

How do I use the 80 20 rule to invest in stocks? ›

In investing, the 80-20 rule generally holds that 20% of the holdings in a portfolio are responsible for 80% of the portfolio's growth. On the flip side, 20% of a portfolio's holdings could be responsible for 80% of its losses.

What is the 50% Rule in stocks? ›

The fifty percent principle is a rule of thumb that anticipates the size of a technical correction. The fifty percent principle states that when a stock or other asset begins to fall after a period of rapid gains, it will lose at least 50% of its most recent gains before the price begins advancing again.

What is the golden Rule of investing in stocks? ›

Warren Buffet's first rule of investing is to never lose money; his second is to never forget the first rule. This golden rule is key for long-term capital protection and growth.

What is the 70% Rule investing? ›

Basically, the rule says real estate investors should pay no more than 70% of a property's after-repair value (ARV) minus the cost of the repairs necessary to renovate the home. The ARV of a property is the amount a home could sell for after flippers renovate it.

Top Articles
Latest Posts
Article information

Author: Francesca Jacobs Ret

Last Updated:

Views: 6405

Rating: 4.8 / 5 (68 voted)

Reviews: 91% of readers found this page helpful

Author information

Name: Francesca Jacobs Ret

Birthday: 1996-12-09

Address: Apt. 141 1406 Mitch Summit, New Teganshire, UT 82655-0699

Phone: +2296092334654

Job: Technology Architect

Hobby: Snowboarding, Scouting, Foreign language learning, Dowsing, Baton twirling, Sculpting, Cabaret

Introduction: My name is Francesca Jacobs Ret, I am a innocent, super, beautiful, charming, lucky, gentle, clever person who loves writing and wants to share my knowledge and understanding with you.