Compound Annual Growth Rate (CAGR) Formula and Calculation :-Investopedia by How reinvesting your profits at the end of the year can impact your investments By Jason Fernando Updated November 12, 2024 Reviewed by Julius Mansa Fact checked by Pete Rathburn

 

What Is the Compound Annual Growth Rate (CAGR)?

The compound annual growth rate is the rate of return that an investment would need to have every year in order to grow from its beginning balance to its ending balance, over a given time interval. The CAGR assumes that any profits were reinvested at the end of each period of the investment’s life span.

Key Takeaways

• The compounded annual growth rate (CAGR) is one of the most accurate ways to calculate and determine returns for anything that can rise or fall in value over time.
• It measures a smoothed rate of return.
• Investors can compare the CAGR of two or more alternatives to evaluate how well one stock performed against other stocks in a peer group or a market index.
• CAGR is thus a good way to evaluate how different investments have performed over time, or against a benchmark.
• The CAGR does not, however, reflect investment risk.

Investopedia / Alex Dos Diaz

How to Calculate Compound Annual Growth Rate (CAGR)

$\begin{array}{cc}{\displaystyle }& {\displaystyle CAGR=({\left(\frac{EV}{BV}\right)}^{\frac{1}{n}}-1)\times 100}\\ {\displaystyle }& {\displaystyle \text{where:}}\\ {\displaystyle }& {\displaystyle EV=\text{Ending value}}\\ {\displaystyle }& {\displaystyle BV=\text{Beginning value}}\\ {\displaystyle }& {\displaystyle n=\text{Number of years}}\end{array}$

CAGR=((

BVEV​

)

n1​

−1)×100

where:EV=Ending valueBV=Beginning valuen=Number of years​

To calculate the CAGR of an investment:

1. Divide the value of an investment at the end of the period by its value at the beginning of that period.
2. Raise the result to an exponent of one divided by the number of years.
3. Subtract one from the subsequent result.
4. Multiply by 100 to convert the answer into a percentage.

The CAGR formula gives an annualized rate of return, which is useful for comparing the performance of different investments over time.

What the CAGR Can Tell You

The compound annual growth rate isn’t a true return rate, but rather a representational figure. It is essentially a number that describes the rate at which an investment would have grown if it had grown at the same rate every year and the profits were reinvested at the end of each year. For stock market investors, this can be particularly useful in comparing the performance of different stocks. The CAGR does not take into account the discount rate, which is critical in assessing the present value of future returns.

In reality, this sort of performance is unlikely. However, the CAGR can be used to smooth returns so that they may be more easily understood and compared to alternative methods.

Example of How to Use CAGR

Imagine you invested $10,000 in a portfolio with the returns outlined below:

• From Jan. 1, 2018, to Jan. 1, 2019, your portfolio grew to $13,000 (or 30% in year one).
• On Jan. 1, 2020, the portfolio was $14,000 (or 7.69% from January 2019 to January 2020).
• On Jan. 1, 2021, the portfolio ended with $19,000 (or 35.71% from January 2020 to January 2021).

We can see that on an annual basis, the year-to-year growth rates of the investment portfolio were quite different as shown in the parentheses.

On the other hand, the compound annual growth rate smooths the investment’s performance and ignores the fact that 2018 and 2020 were vastly different from 2019. The CAGR over that period was 23.86% and can be calculated as follows:

$CAGR={\left(\frac{\mathrm{\$}19,000}{\mathrm{\$}10,000}\right)}^{\frac{1}{3}}-1\times 100=23\mathrm{.}86\mathrm{\%}$

CAGR=(

$10,000$19,000​

)

31​

−1×100=23.86%

The CAGR of 23.86% over the three-year investment period can help an investor compare alternatives for their capital or make forecasts of future values. For example, imagine an investor is comparing the performance of two uncorrelated investments.

In any given year during the period, one investment may be rising while the other falls. This could be the case when comparing high-yield bonds to stocks, or a real estate investment to emerging markets. Using CAGR would smooth the annual return over the period so the two alternatives would be easier to compare.

As another example, let’s say an investor bought 55 shares of Amazon.com (AMZN) stock in December 2017 at $1,180 per share, for a total investment of $64,900. After three years, in December 2020, the stock has risen to $3,200 per share, and the investor’s investment is now worth $176,000.

1

 What is the CAGR?

Using the CAGR formula, we know that we need the:

• Ending Balance: $176,000
• Beginning Balance: $64,900
• Number of Years: 3

So to calculate the CAGR for this simple example, we would enter that data into the formula as follows: [($176,000 / $64,900) ^ (1/3)] - 1 = 39.5%.

Additional CAGR Uses

The CAGR can be used to calculate the average growth of a single investment. As we saw in our example above, due to market volatility, the year-to-year growth of an investment will likely appear erratic and uneven.

For example, an investment may increase in value by 8% in one year, decrease in value by -2% the following year, and increase in value by 5% in the next. CAGR helps smooth returns when growth rates are expected to be volatile and inconsistent.

Comparing Investments

The CAGR produces a geometric mean which can be used to compare different investment types with one another. For example, suppose that in 2015, an investor placed $10,000 into an account for five years with a fixed annual interest rate of 1% and another $10,000 into a stock mutual fund. The rate of return in the stock fund will be uneven over the next few years, so a comparison between the two investments would be difficult.

Assume that at the end of the five-year period, the savings account’s balance is $10,510.10 and, although the other investment has grown unevenly, the ending balance in the stock fund was $15,348.52. Using the CAGR to compare the two investments can help an investor understand the difference in returns:

$\text{Savings Account CAGR}={\left(\frac{\mathrm{\$}10,510\mathrm{.}10}{\mathrm{\$}10,000}\right)}^{\frac{1}{5}}-1\times 100=1\mathrm{.}00\mathrm{\%}$

Savings Account CAGR=(

$10,000$10,510.10​

)

51​

−1×100=1.00%

And:

$\text{Stock fund CAGR}={\left(\frac{\mathrm{\$}15,348\mathrm{.}52}{\mathrm{\$}10,000}\right)}^{\frac{1}{5}}-1\times 100=8\mathrm{.}95\mathrm{\%}$

Stock fund CAGR=(

$10,000$15,348.52​

)

51​

−1×100=8.95%

On the surface, the stock fund may look like a better investment, with nearly nine times the return of the savings account. On the other hand, one of the drawbacks of the CAGR is that by smoothing the returns, the CAGR cannot tell an investor how volatile or risky the stock fund was. However, the CAGR can be used in the MAR ratio, which adjusts for risk. Using the CAGR alongside metrics like net present value (NPV) provides a more comprehensive view of an investment’s potential.

Track Performance

The CAGR can also be used to track the performance of various business measures of one or multiple companies alongside one another. For example, over a five-year period, Big-Sale Stores’ market share CAGR was 1.82%, but its customer satisfaction CAGR over the same period was -0.58%. In this way, comparing the CAGRs of measures within a company reveals strengths and weaknesses.

Detect Weaknesses and Strengths

Comparing the CAGRs of business activities across similar companies will help evaluate competitive weaknesses and strengths. For example, Big-Sale’s customer satisfaction CAGR might not seem so low compared with SuperFast Cable’s customer satisfaction CAGR of -6.31% during the same period.

How Investors Use the CAGR

Understanding the formula used to calculate CAGR is an introduction to many other ways that investors evaluate past returns or estimate future profits. The formula can be manipulated algebraically into a formula to find the present value or future value of money, or to calculate a hurdle rate of return.

For example, imagine that an investor knows that they need $50,000 for a child’s college education in 18 years and they have $15,000 to invest today. How much does the average rate of return need to be to reach that objective? The CAGR calculation can be used to find the answer to this question as follows:

$\text{Required Return}={\left(\frac{\mathrm{\$}50,000}{\mathrm{\$}15,000}\right)}^{\frac{1}{18}}-1\times 100=6\mathrm{.}90\mathrm{\%}$

Required Return=(

$15,000$50,000​

)

181​

−1×100=6.90%

This version of the CAGR formula is just a rearranged present value and future value equation. For example, if an investor knew that they needed $50,000 and they felt it was reasonable to expect an 8% annual return on their investment, they could use this formula to find out how much they needed to invest to meet their goal.

What Is a Good CAGR?

What counts as a good CAGR will depend on the context. But generally speaking, investors will evaluate this by thinking about their opportunity cost as well as the riskiness of the investment. For example, if a company grew by 25% in an industry with an average CAGR closer to 30%, then its results might seem lackluster by comparison. But if the industry-wide growth rates were lower, such as 10% or 15%, then its CAGR might be very impressive.

In general, a higher CAGR is better.

Modifying the CAGR Formula

An investment is rarely made on the first day of the year and then sold on the last day of the year. Imagine an investor who wants to evaluate the CAGR of a $10,000 investment that was entered on June 1, 2013, and sold for $16,897.14 on Sept. 9, 2018.

Before the CAGR calculation can be performed, the investor will need to know the fractional remainder of the holding period. They held the position for 213 days in 2013, a full year in 2014, 2015, 2016, and 2017, and 251 days in 2018. This investment was held for 5.271 years, which is calculated by the following:

• 2013 = 213 days
• 2014 = 365
• 2015 = 365
• 2016 = 365
• 2017 = 365
• 2018 = 251

The total number of days that the investment was held was 1,924 days. To calculate the number of years, divide the total number of days by 365 (1,924/365), which equals 5.271 years.

The total number of years that the investment was held can be placed in the denominator of the exponent inside CAGR’s formula as follows:

$\text{Investment CAGR}={\left(\frac{\mathrm{\$}16,897\mathrm{.}14}{\mathrm{\$}10,000}\right)}^{\frac{1}{5\mathrm{.}271}}-1\times 100=10\mathrm{.}46\mathrm{\%}$

Investment CAGR=(

$10,000$16,897.14​

)

5.2711​

−1×100=10.46%

Smooth Rate of Growth Limitation

The most important limitation of the CAGR is that because it calculates a smoothed rate of growth over a period, it ignores volatility and implies that the growth during that time was steady. Returns on investments are uneven over time, except for bonds that are held to maturity, deposits, and similar investments.

Also, the CAGR does not account for when an investor adds funds to a portfolio or withdraws funds from the portfolio over the period being measured.

For example, if an investor had a portfolio for five years and injected funds into the portfolio during the five-year period, then the CAGR would be inflated. The CAGR would calculate the rate of return based on the beginning and ending balances over the five years, and would essentially count the deposited funds as part of the annual growth rate, which would be inaccurate.

Other CAGR Limitations

Besides the smoothed rate of growth, the CAGR has other limitations. A second limitation when assessing investments is that no matter how steady the growth of a company or investment has been in the past, investors cannot assume that the rate will remain the same in the future. The shorter the time frame used in the analysis, the less likely it will be for the realized CAGR to meet the expected CAGR when relying on historical results.

A third limitation of the CAGR is a limitation of representation. Say that an investment fund was worth $100,000 in 2016, $71,000 in 2017, $44,000 in 2018, $81,000 in 2019, and $126,000 in 2020. If the fund managers represented in 2021 that their CAGR was a whopping 42.01% over the past three years, they would be technically correct. They would, however, be omitting some very important information about the fund’s history, including the fact that the fund’s CAGR over the past five years was a modest 4.73%.

CAGR vs. IRR

The CAGR measures the return on an investment over a certain period of time. The internal rate of return (IRR) also measures investment performance but is more flexible than the CAGR.

The most important distinction is that the CAGR is straightforward enough that it can be calculated by hand. In contrast, more complicated investments and projects, or those that have many different cash inflows and outflows, are best evaluated using IRR. To back into the IRR, a financial calculator, Excel, or portfolio accounting system is ideal.

Those interested in learning more about CAGR and other financial topics may want to consider enrolling in one of the best investing courses currently available.

What Is an Example of Compound Annual Growth Rate (CAGR)?

The CAGR is a measurement used by investors to calculate the rate at which a quantity grew over time. The word “compound” denotes the fact that the CAGR takes into account the effects of compounding, or reinvestment, over time. For example, suppose you have a company with revenue that grew from $3 million to $30 million over a span of 10 years. In that scenario, the CAGR would be approximately 25.89%.

What Is the Difference Between the CAGR and a Growth Rate?

The main difference between the CAGR and a growth rate is that the CAGR assumes the growth rate was repeated, or “compounded,” each year, whereas a traditional growth rate does not. Many investors prefer the CAGR because it smooths out the volatile nature of year-by-year growth rates. For instance, even a highly profitable and successful company will likely have several years of poor performance during its life. These bad years could have a large effect on individual years’ growth rates but would have a relatively small impact on the company’s CAGR.

Can the CAGR Be Negative?

Yes. A negative CAGR would indicate losses over time rather than gains.

What Is Risk-Adjusted CAGR?

To compare the performance and risk characteristics among various investment alternatives, investors can use a risk-adjusted CAGR. A simple method for calculating a risk-adjusted CAGR is to multiply the CAGR by one minus the investment’s standard deviation. If the standard deviation (i.e., its risk) is zero, then the risk-adjusted CAGR is unaffected. The larger the standard deviation, the lower the risk-adjusted CAGR will be.

The Bottom Line

CAGR is a valuable metric for investors to gauge the performance of their investments over time. By smoothing out annual returns, it provides a clearer picture of an investment's growth trajectory. However, while CAGR can help compare different investments and predict future values, it does not account for volatility or risk. Investors should use CAGR alongside other measures to make well-informed decisions, understanding its limitations in reflecting the full scope of investment performance.

• The compounded annual growth rate (CAGR) is one of the most accurate ways to calculate and determine returns for anything that can rise or fall in value over time.
• It measures a smoothed rate of return.
• Investors can compare the CAGR of two or more alternatives to evaluate how well one stock performed against other stocks in a peer group or a market index.
• CAGR is thus a good way to evaluate how different investments have performed over time, or against a benchmark.
• The CAGR does not, however, reflect investment risk.

Viral video: Woman confronts ‘vacationing’ Justin Trudeau, shakes his hand and says ‘Please get the f**k out’ | Watch :-livemint

 

This holiday season, Justin Trudeau's ski vacation in British Columbia was marred by public mockery and confrontations, a stark departure from his past popularity

The New Year has not been a particularly happy one for Justin Trudeau. During his Christmas vacation, which may be his last as Canada’s prime minister, Trudeau encountered a challenge he wasn’t fully quite ready for.

Amid the heated political climate in the country, the prime minister headed to a ski resort in British Columbia, seeking a few peaceful days of holiday. However, Trudeau’s trip was marred by displays of public mockery and hostility.

This was likely Trudeau’s final Christmas vacation as prime minister, with Canada set to hold general elections later this year.

A viral video shows a woman confronting Justin Trudeau in the parking lot of a resort in Rossland. The woman, who called out ‘Mr Prime Minister’, shook his hand and said, “Please get the f**k out of B.C. You s**k!”

Unsure of how to react, Trudeau chuckled and said, “Have a wonderful day, ma'am.”

In another viral video, Trudeau was mocked by a fellow diner during his vacation. In the video, a diner clandestinely showed a smartphone displaying the infamous image of Justin Trudeau in blackface makeup before panning over to show the prime minister at an adjacent table.

Trudeau would have witnessed more hate had he walked through the resort on Saturday night. A local music duo had arrived at the resort to sing anti-Trudeau folk songs.

In a Facebook video posted by Castlegar, BC’s Doreen Court, she sings, “Hey, Hey Trudeau, you know it’s time to go, get out of our government and take your walk in the snow.”

Goosebumps! Indian Army shares video of soldiers braving bone-chilling Ladakh weather :-livemint

 

The Indian Army says the rugged, treacherous terrain, often covered in snow or turning into a swamp during the monsoon, presents constant challenges, yet its soldiers persevere with unwavering commitment.

Sharing about the incredible sacrifices made by soldiers, the Indian Army on Wednesday said despite facing extreme weather conditions in areas such as Jammu and Kashmir and Ladakh, its troops remained steadfast in their duty.

“As we welcome the New Year, it's important to take a moment to reflect on the incredible sacrifices made by our soldiers, especially those guarding the Line of Control (LoC) in Jammu & Kashmir,” said the Indian Army.

“The Indian Army, despite facing extreme weather conditions — from searing heat in the summer in Rajasthan to bone-chilling cold in the winter in Ladakh, J&K, Himachal, Arunachal Pradesh and Sikkim — remains steadfast in its duty,” it added.

The Indian Army further said: “The rugged, treacherous terrain, often covered in snow or turning into a swamp during the monsoon, presents constant challenges, yet our soldiers persevere with unwavering commitment.”

India's power consumption increases nearly 6% to 130.40 bn units in Dec :-The peak power demand touched an all-time high of about 250 GW in May 2024. The previous all-time high peak power demand of 243.27 GW was recorded in September 2023 :-The Business Standard

 

The highest supply in a day (peak power demand met) also rose to 224.16 GW in December 2024 from 213.62 GW.

India's power consumption rose nearly 6 per cent to 130.40 billion units (BU) in December as compared to the year-ago month.

In December 2023, power consumption was 123.17 BU, as per government data.

The highest supply in a day (peak power demand met) also rose to 224.16 GW in December 2024 from 213.62 GW in the year-ago period.

The peak power demand touched an all-time high of about 250 GW in May 2024. The previous all-time high peak power demand of 243.27 GW was recorded in September 2023.

Earlier this year, the power ministry projected a peak power demand of 235 GW during the day and 225 GW during evening hours for May 2024 while 240 GW during daytime and 235 GW in the evening hours for June 2024.

10 killed, several injured as truck rams into crowd in New Orleans; ‘terrorist attack,’ says mayor US New Orleans Car Accident News: Several videos of the incident have been circulating on social media, showing multiple casualties on the ground, as per BBC reports. :-The Indian Express

 

US New Orleans Car Accident: At least 10 people were killed and 30 more were injured Wednesday after a truck drove into a crowd on Bourbon Street in New Orleans, according to New Orleans city officials, BBC reported.

The truck crashed into the crowd at high speed, and the driver then exited the vehicle and began firing a weapon, prompting police to return fire, CBS News reported, citing witnesses. According to reports the injured had been taken to five local hospitals.

New Orleans Mayor LaToya Cantrell called the incident as a “terrorist attack.” However, the FBI is investigating what occurred early Wednesday, when the vehicle drove into a crowd.

“Initial reports show a car may have plowed into a group of people. Injuries are unknown but there are reported fatalities,” New Orleans Police Department spokesperson told CBS News. Several videos of the incident circulating on social media show multiple casualties on the ground, as per BBC reports.

Nola Ready, responsible for emergency preparedness in the City of New Orleans, posted on X, “There has been a mass casualty incident on Canal and Bourbon Street. Get yourself away from the area. ”

The incident occurred towards the end of New Year’s celebrations in the city and hours before the kickoff of the AllState Bowl, a college football quarterfinal held in the city’s Caesars Superdome — thousands are expected to be in attendance.

The city has witnessed shootings and cars colliding with crowds at past parades — two people were killed and 10 others were injured in two separate incidents along a New Orleans parade route and celebration in November 2024, according to local media reports.

As H-1B debate heats up, Americans say US doesn't need more foreign workers :-ET

 

Amid the heated debate over the H-1B visa program, a new Rasmussen Reports survey reveals that most Americans believe the US already has enough skilled workers to train and hire for white-collar jobs, negating the need for more foreign workers.

Conducted in November among 1,000 likely voters, the survey highlights widespread public resistance to expanding the H-1B program.

According to the survey, 60% of Americans believe the U.S. has enough domestic talent to meet the demand for white-collar jobs, negating the need for foreign worker programs. This perspective is strongest among Republicans, with 72% expressing opposition. Similar sentiments were echoed by 63% of swing voters and 47% of Democrats, while only 26% of respondents supported expanding the program.

Large companies, including Amazon, Google, and Tesla, have relied on H-1B visas to fill key positions, allowing temporary residency and employment for foreign workers in the US. While some argue the program addresses critical labor gaps, others claim it undermines opportunities for American workers and suppresses wages.

MAGA divide over H-1B policy

The H-1B program, which allows US companies to hire foreign workers for specialized roles, has sparked intense debate among MAGA leaders. While tech advocates like Elon Musk and Vivek Ramaswamy argue for program expansion to address labor shortages, traditional MAGA voices such as Steve Bannon, Nikki Haley, and Laura Loomer oppose the move.

Musk emphasized the program's role in meeting workforce demands, with companies like Amazon, Google, Meta, and Tesla benefiting significantly from H-1B hires in 2024. However, he has also called for reforms to make H-1B hiring more expensive, ensuring it doesn’t become a pathway for cheap labor.

Trump’s stand on H-1B visas

President-elect Donald Trump has reiterated his support for the H-1B program despite earlier restrictions implemented during his first term. “I’ve always liked the visas; I’ve always been in favor of the visas. That’s why we have them,” Trump said, noting that his businesses have extensively used H-1B visas.

The divide became more pronounced after Trump nominated Musk and Ramaswamy to co-lead the newly established Department of Government Efficiency (DOGE), sparking further criticism from immigration hardliners within the MAGA coalition.

Read more at:
https://economictimes.indiatimes.com/nri/latest-updates/as-h-1b-debate-heats-up-americans-say-us-doesnt-need-more-foreign-workers/articleshow/116846217.cms?utm_source=contentofinterest&utm_medium=text&utm_campaign=cppst

ign=cppst

GST collection rises 7.3 pc to Rs 1.77 lakh crore in December :-ET

 

India’s gross Goods and Services Tax (GST) collection grew 7.3% year-on-year in December, reaching ₹1.77 lakh crore, as per data released by the government on Wednesday. This marks an increase from ₹1.65 lakh crore collected in the same month last year.

The revenue distribution for December includes ₹32,836 crore from Central GST, ₹40,499 crore from State GST, ₹47,783 crore from Integrated GST, and ₹11,471 crore from cess.

Read more at:
https://economictimes.indiatimes.com/news/economy/finance/gst-collection-rises-7-3-pc-to-rs-1-77-lakh-crore-in-december/articleshow/116854682.cms?utm_source=contentofinterest&utm_medium=text&utm_campaign=cppst

Trade war with India will not be in the interest of US, says RIS Read more at: https://economictimes.indiatimes.com/news

 

Initiating trade war with India will not be in the interest of the US, as seen in the past, the Research and Information System (RIS) for developing countries said on Tuesday.

"Given the past experience, new policy shifts may cause temporary setbacks in the short term, but these are often counterbalanced in subsequent years," it said in its policy brief on Trade, Tariff and Trump.

"This resilience stems from the proactive responses of affected countries, which include measures such as unilateral tariff hikes, appeals to the WTO's dispute settlement mechanisms, and other strategic interventions," it added.

According to the RIS policy brief, these efforts have proven instrumental in mitigating the adverse impacts of US trade policies, ultimately tempering the pressures exerted by the US administration.

Though apprehensive that the Trump 2.0 administration can target India because of the high trade surplus India has with the US, RIS said structural transformations require time.

"Under the Trump administration, a sharp decline in the level of India's trade surplus with the US was recorded in the second year of his presidency, notably in 2018. However, downturn was short-lived, and India's bilateral trade surplus with the US began a consistent upward trajectory until the conclusion of Trump's tenure in 2021," it said.

Read more at:
https://economictimes.indiatimes.com/news/economy/foreign-trade/trade-war-with-india-will-not-be-in-the-interest-of-us-says-ris/articleshow/116843411.cms?utm_source=contentofinterest&utm_medium=text&utm_campaign=cppst

2025 A YEAR TO REMEMBER AS MATHEMATICALMARVEL

 

The year 2025 is called a mathematical wonder. Why?

 Let’s break it down. 2025 is a perfect square of 45 (45×45 = 2025). 

It’s also the product of two squares (9 and 5). 

Furthermore, it’s the sum of three squares (40×40 + 20×20 + 5×5 = 2025).

 On top of that, 2025 is the sum of the cubes of digits from 1 to 9 (1³ + 2³ + 3³ + 4³ + 5³ + 6³ + 7³ + 8³ + 9³ = 2025). 

It marks the first square year since 1936. It’s also the only square year our generation will experience, as the next square year will be in 2116, 92 years from now. Let’s make 2025 a year to remember, a mathematical marvel!