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What Is an Amortization Schedule? How to Calculate with Formula

Written by admin. Posted in A, Financial Terms Dictionary

What Is an Amortization Schedule? How to Calculate With Formula

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 Period Beginning Loan Balance Payment Interest Principal Ending Loan Balance
Month or period Amount of debt owed at the start of the month of period Amount due each month (often a fixed amount over the term of the loan) Amount of interest included in the payment (loan balance * 1/12 of interest) Amount of principal included in loan payment (Payment – Interest) Amount of debt owed at the end of the month or period (Beginning Loan Balance – Principal)
  • The period is the timing of each loan payment, often represented on a monthly basis. However, each row on an amortization represents a payment so if a loan is due bi-weekly or quarterly, the period will be the same. This column helps a borrower and lender understand which payments will be broken down in what ways. This may either be shown as a payment number (i.e., Payment 1, Payment 2, etc.) or a date (i.e. 1/1/2023, 2/1/2023, etc.).
  • The beginning loan balance is amount of debt owed at the beginning of the period. This amount is either the original amount of the loan or the amount carried over from the prior month (last month’s ending loan balance equals this month’s beginning loan balance).
  • The payment is the monthly obligation calculated above. This will often remain constant over the term of the loan. Though you usually calculate the payment amount before calculating interest and principal, payment is equal to the sum of principal and interest.
  • The interest portion is the amount of the payment that gets applied as interest expense. This is often calculated as the outstanding loan balance multiplied by the interest rate attributable to this period’s portion of the rate. For example, if a payment is owed monthly, this interest rate may be calculated as 1/12 of the interest rate multiplied by the beginning balance. Always be mindful of how a lender calculates, applies, and compounds your annual percentage rate as this impacts your schedule. As the outstanding loan balance decreases over time, less interest should be charged each period.
  • The principal portion is simply the left over amount of the payment. This is the total payment amount less the amount of interest expense for this period. As the outstanding loan balance decreases over time, less interest will be charged, so the value of this column should increase over time.
  • The ending loan balance is the difference between the beginning loan balance and the principal portion. This represents the new debt balance owed based on the payment made for the new period.

Amortization of Intangible Assets

Amortization can also refer to the amortization of intangibles. In this case, amortization is the process of expensing the cost of an intangible asset over the projected life of the asset. It measures the consumption of the value of an intangible asset, such as goodwill, a patent, a trademark, or copyright.

Amortization is calculated in a similar manner to depreciation—which is used for tangible assets, such as equipment, buildings, vehicles, and other assets subject to physical wear and tear—and depletion, which is used for natural resources.

When businesses amortize expenses over time, they help tie the cost of using an asset to the revenues that it generates in the same accounting period, in accordance with generally accepted accounting principles (GAAP). For example, a company benefits from the use of a long-term asset over a number of years. Thus, it writes off the expense incrementally over the useful life of that asset.

The amortization of intangibles is also useful in tax planning. The Internal Revenue Service (IRS) allows taxpayers to take a deduction for certain expenses: geological and geophysical expenses incurred in oil and natural gas exploration, atmospheric pollution control facilities, bond premiums, research and development (R&D), lease acquisition, forestation and reforestation, and intangibles, such as goodwill, patents, copyrights, and trademarks.

The IRS has schedules that dictate the total number of years in which to expense tangible and intangible assets for tax purposes.

Why Is Amortization Important?

Amortization is important because it helps businesses and investors understand and forecast their costs over time. In the context of loan repayment, amortization schedules provide clarity into what portion of a loan payment consists of interest versus principal. This can be useful for purposes such as deducting interest payments for tax purposes. It is also useful for future planning to understand what a company’s future debt balance will be in the future after a series of payments have already been made.

Amortizing intangible assets is important because it can reduce a business’s taxable income, and therefore its tax liability, while giving investors a better understanding of the company’s true earnings. Intangible assets also have a finite useful life; over time, trademarks or patents may lose their value due to obsolescence. Amortizing intangible assets is also a reflection of how a company has “used up” the benefit of these assets.

Amortization vs. Depreciation

Amortization and depreciation are similar concepts, in that both attempt to capture the cost of holding an asset over time. The main difference between them, however, is that amortization refers to intangible assets, whereas depreciation refers to tangible assets. Examples of intangible assets include trademarks and patents; tangible assets include equipment, buildings, vehicles, and other assets subject to physical wear and tear.

Another difference is the accounting treatment in which different assets are reduced on the balance sheet. Amortizing an intangible asset is performed by directly crediting (reducing) that specific asset account. Alternatively, depreciation is recorded by crediting an account called accumulated depreciation, a contra asset account. The historical cost fixed assets remains on a company’s books; however, the company also reports this contra asset amount to report a net reduced book value amount.

Last, the calculation of each can be different. This is especially true when comparing depreciation to the amortization of a loan. Intangible assets are often amortized over their useful life using the straight-line method, while fixed assets often use a much more broad set of calculation methods (i.e., declining balance method, double-declining balance method, sum-of-the-years’ digits method, or the units of production method).

Example of Amortization

Let’s look at a four-year, $30,000 auto loan at 3% interest. The monthly payment is going to be $664.03. That is arrived at as follows:


$ 30 , 000 × ( 0.0025 × ( 1.0025 ÷ 48 ) 1.0025 ÷ 48 1 ) \begin{aligned}&\$30,000 \times \Bigg ( \frac { 0.0025 \times (1.0025 \div 48) }{ 1.0025 \div 48 } – 1 \Bigg ) \\\end{aligned}
$30,000×(1.0025÷480.0025×(1.0025÷48)1)

In the first month, $75 of the $664.03 monthly payment goes to interest.


$ 30 , 000  loan balance × 3 %  interest rate ÷ 12  months \begin{aligned}&\$30,000 \ \text{loan balance} \times 3\% \ \text{interest rate} \div 12 \ \text{months} \\\end{aligned}
$30,000 loan balance×3% interest rate÷12 months

The remaining $589.03 goes toward principal.


$ 664.03  total monthly payment $ 75  interest payment \begin{aligned}&\$664.03 \ \text{total monthly payment} – \$75 \ \text{interest payment} \\ \end{aligned}
$664.03 total monthly payment$75 interest payment

The total payment stays the same each month, while the portion going to principal increases and the portion going to interest decreases. In the final month, only $1.66 is paid in interest, because the outstanding loan balance at that point is very minimal compared with the starting loan balance.

Loan Amortization Schedule
Period Total Payment Due Computed Interest Due Principal Due Principal Balance
        $30,000
1 $664.03 $75 $589.03 $29,410.97
2 $664.03 $73.53 $590.50 $28,820.47
3 $664.03 $72.05 $591.98 $28,228.49
4 $664.03 $70.57 $593.46 $27,635.03
5 $664.03 $69.09 $594.94 $27,040.09
6 $664.03 $67.60 $596.43 $26,443.66
7 $664.03 $66.11 $597.92 $25,845.74
8 $664.03 $64.61 $599.42 $25,246.32
9 $664.03 $63.12 $600.91 $24,645.41
10 $664.03 $61.61 $602.42 $24,042.99
11 $664.03 $60.11 $603.92 $23,439.07
12 $664.03 $58.60 $605.43 $22,833.64
13 $664.03 $57.08 $606.95 $22,226.69
14 $664.03 $55.57 $608.46 $21,618.23
15 $664.03 $54.05 $609.98 $21,008.24
16 $664.03 $52.52 $611.51 $20,396.73
17 $664.03 $50.99 $613.04 $19,783.69
18 $664.03 $49.46 $614.57 $19,169.12
19 $664.03 $47.92 $616.11 $18,553.02
20 $664.03 $46.38 $617.65 $17,935.37
21 $664.03 $44.84 $619.19 $17,316.18
22 $664.03 $43.29 $620.74 $16,695.44
23 $664.03 $41.74 $622.29 $16,073.15
24 $664.03 $40.18 $623.85 $15,449.30
25 $664.03 $38.62 $625.41 $14,823.89
26 $664.03 $37.06 $626.97 $14,196.92
27 $664.03 $35.49 $628.54 $13,568.38
28 $664.03 $33.92 $630.11 $12,938.28
29 $664.03 $32.35 $631.68 $12,306.59
30 $664.03 $30.77 $633.26 $11,673.33
31 $664.03 $29.18 $634.85 $11,038.48
32 $664.03 $27.60 $636.43 $10,402.05
33 $664.03 $26.01 $638.02 $9,764.02
34 $664.03 $24.41 $639.62 $9,124.40
35 $664.03 $22.81 $641.22 $8,483.18
36 $664.03 $21.21 $642.82 $7,840.36
37 $664.03 $19.60 $644.43 $7,195.93
38 $664.03 $17.99 $646.04 $6,549.89
39 $664.03 $16.37 $647.66 $5,902.24
40 $664.03 $14.76 $649.27 $5,252.96
41 $664.03 $13.13 $650.90 $4,602.06
42 $664.03 $11.51 $652.52 $3,949.54
43 $664.03 $9.87 $654.16 $3,295.38
44 $664.03 $8.24 $655.79 $2,639.59
45 $664.03 $6.60 $657.43 $1,982.16
46 $664.03 $4.96 $659.07 $1,323.09
47 $664.03 $3.31 $660.72 $662.36
48 $664.03 $1.66 $662.36 $0.00

Frequently Asked Questions

What Is Negative Amortization?

Negative amortization is when the size of a debt increases with each payment, even if you pay on time. This happens because the interest on the loan is greater than the amount of each payment. Negative amortization is particularly dangerous with credit cards, whose interest rates can be as high as 20% or even 30%. In order to avoid owing more money later, it is important to avoid over-borrowing and to pay your debts as quickly as possible.

What Does Amortization Mean for Intangible Assets?

Amortization measures the declining value of intangible assets, such as goodwill, trademarks, patents, and copyrights. This is calculated in a similar manner to the depreciation of tangible assets, like factories and equipment. When businesses amortize intangible assets over time, they are able to tie the cost of those assets with the revenue generated over each accounting period and deduct the costs over the lifetime of the asset.

Why Is Amortization Important in Accounting?

Amortization helps businesses and investors understand and forecast their costs over time. In the context of loan repayment, amortization schedules provide clarity into what portion of a loan payment consists of interest versus principal. This can be useful for purposes such as deducting interest payments for tax purposes. Amortizing intangible assets is also important because it can reduce a company’s taxable income and therefore its tax liability, while giving investors a better understanding of the company’s true earnings.

How Do You Amortize a Loan?

A loan is amortized by determining the monthly payment due over the term of the loan. Then, prepare an amortization schedule that clearly identifies what portion of each month’s payment is attributable towards interest and what portion of each month’s payment is attributable towards principal.

Since part of the payment will theoretically be applied to the outstanding principal balance, the amount of interest paid each month will decrease. Since your payment should theoretically remain the same each month, more of your payment each month will apply to principal, thereby paying down the amount you borrowed over time.

The Bottom Line

Amortization is a technique of gradually reducing an account balance over time. When amortizing loans, a gradually escalating portion of the monthly debt payment is applied to the principal. When amortizing intangible assets, amortization is similar to depreciation where a fixed percentage of an asset’s book value is reduced each month. This technique is used to reflect how the benefit of an asset is received by a company over time.

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Angel Investor Definition and How It Works

Written by admin. Posted in A, Financial Terms Dictionary

Allowance for Bad Debt: Definition and Recording Methods

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What Is an Angel Investor?

An angel investor (also known as a private investor, seed investor or angel funder) is a high-net-worth individual who provides financial backing for small startups or entrepreneurs, typically in exchange for ownership equity in the company. Often, angel investors are found among an entrepreneur’s family and friends. The funds that angel investors provide may be a one-time investment to help the business get off the ground or an ongoing injection to support and carry the company through its difficult early stages.

Key Takeaways

  • An angel investor is usually a high-net-worth individual who funds startups at the early stages, often with their own money.
  • Angel investing is often the primary source of funding for many startups who find it more appealing than other, more predatory, forms of funding.
  • The support that angel investors provide startups fosters innovation which translates into economic growth.
  • These types of investments are risky and usually do not represent more than 10% of the angel investor’s portfolio.

Understanding Angel Investors

Angel investors are individuals who seek to invest at the early stages of startups. These types of investments are risky and usually do not represent more than 10% of the angel investor’s portfolio. Most angel investors have excess funds available and are looking for a higher rate of return than those provided by traditional investment opportunities.

Angel investors provide more favorable terms compared to other lenders, since they usually invest in the entrepreneur starting the business rather than the viability of the business. Angel investors are focused on helping startups take their first steps, rather than the possible profit they may get from the business. Essentially, angel investors are the opposite of venture capitalists.

Angel investors are also called informal investors, angel funders, private investors, seed investors or business angels. These are individuals, normally affluent, who inject capital for startups in exchange for ownership equity or convertible debt. Some angel investors invest through crowdfunding platforms online or build angel investor networks to pool capital together.

Origins of Angel Investors

The term “angel” came from the Broadway theater, when wealthy individuals gave money to propel theatrical productions. The term “angel investor” was first used by the University of New Hampshire’s William Wetzel, founder of the Center for Venture Research. Wetzel completed a study on how entrepreneurs gathered capital.

Who Can Be an Angel Investor?

Angel investors are normally individuals who have gained “accredited investor” status but this isn’t a prerequisite. The Securities and Exchange Commission (SEC) defines an “accredited investor” as one with a net worth of $1M in assets or more (excluding personal residences), or having earned $200k in income for the previous two years, or having a combined income of $300k for married couples. Conversely, being an accredited investor is not synonymous with being an angel investor.

Essentially these individuals both have the finances and desire to provide funding for startups. This is welcomed by cash-hungry startups who find angel investors to be far more appealing than other, more predatory, forms of funding.

Sources of Funding

Angel investors typically use their own money, unlike venture capitalists who take care of pooled money from many other investors and place them in a strategically managed fund.

Though angel investors usually represent individuals, the entity that actually provides the funds may be a limited liability company (LLC), a business, a trust or an investment fund, among many other kinds of vehicles.

Investment Profile

Angel investors who seed startups that fail during their early stages lose their investments completely. This is why professional angel investors look for opportunities for a defined exit strategy, acquisitions or initial public offerings (IPOs).

The effective internal rate of return for a successful portfolio for angel investors is approximately 22%. Though this may look good for investors and seem too expensive for entrepreneurs with early-stage businesses, cheaper sources of financing such as banks are not usually available for such business ventures. This makes angel investments perfect for entrepreneurs who are still financially struggling during the startup phase of their business.

Angel investing has grown over the past few decades as the lure of profitability has allowed it to become a primary source of funding for many startups. This, in turn, has fostered innovation which translates into economic growth.

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Annual Equivalent Rate (AER): Definition, Formula, Examples

Written by admin. Posted in A, Financial Terms Dictionary

Annual Equivalent Rate (AER): Definition, Formula, Examples

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What Is the Annual Equivalent Rate (AER)?

The annual equivalent rate (AER) is the interest rate for a savings account or investment product that has more than one compounding period. AER is calculated under the assumption that any interest paid is included in the principal payment’s balance and the next interest payment will be based on the slightly higher account balance.

Key Takeaways

  • The annual equivalent rate (AER) is the actual interest rate an investment, loan, or savings account will yield after accounting for compounding.
  • AER is also known as the effective annual interest rate or the annual percentage yield (APY).
  • The AER will be higher than the stated or nominal rate if there is more than one compounding period a year.

The AER method means that interest can be compounded several times in a year, depending on the number of times that interest payments are made.

AER is also known as the effective annual interest rate or the annual percentage yield (APY).

The AER is the actual interest rate that an investor will earn for an investment, a loan, or another product, based on compounding. The AER reveals to investors what they can expect to return from an investment (the ROI)—the actual return of the investment based on compounding, which is more than the stated, or nominal, interest rate.

Assuming that interest is calculated—or compounded—more than once a year, the AER will be higher than the stated interest rate. The more compounding periods, the greater the difference between the two will be.

Formula for the AER


Annual equivalent rate = ( 1 + r n ) n 1 where: n = The number of compounding periods (times per year interest is paid) r = The stated interest rate \begin{aligned} &\text{Annual equivalent rate}=\left(1 + \frac{r}{n}\right)^n-1\\ &\textbf{where:}\\ &n=\text{The number of compounding periods (times per year interest is paid)}\\ &r = \text{The stated interest rate}\\ \end{aligned}
Annual equivalent rate=(1+nr)n1where:n=The number of compounding periods (times per year interest is paid)r=The stated interest rate

How to Calculate the AER

To calculate AER:

  1. Divide the stated interest rate by the number of times a year that interest is paid (compounded) and add one.
  2. Raise the result to the number of times a year that interest is paid (compounded)
  3. Subtract one from the subsequent result.

The AER is displayed as a percentage (%).

Example of AER

Let’s look at AER in both savings accounts and bonds.

For a Savings Account

Assume an investor wishes to sell all the securities in their investment portfolio and place all the proceeds in a savings account. The investor is deciding between placing the proceeds in Bank A, Bank B, or Bank C, depending on the highest rate offered. Bank A has a quoted interest rate of 3.7% that pays interest on an annual basis. Bank B has a quoted interest rate of 3.65% that pays interest quarterly, and Bank C has a quoted interest rate of 3.7% that pays interest semi-annually.

The stated interest rate paid on an account offering monthly interest may be lower than the rate on an account offering only one interest payment per year. However, when interest is compounded, the former account may offer higher returns than the latter account. For example, an account offering a rate of 6.25% paid annually may look more attractive than an account paying 6.12% with monthly interest payments. However, the AER on the monthly account is 6.29%, as opposed to an AER of 6.25% on the account with annual interest payments.

Therefore, Bank A would have an annual equivalent rate of 3.7%, or (1 + (0.037 / 1))1 – 1. Bank B has an AER of 3.7% = (1 + (0.0365 / 4))4 – 1, which is equivalent to that of Bank A even though Bank B is compounded quarterly. It would thus make no difference to the investor if they placed their cash in Bank A or Bank B.

On the other hand, Bank C has the same interest rate as Bank A, but Bank C pays interest semi-annually. Consequently, Bank C has an AER of 3.73%, which is more attractive than the other two banks’ AER. The calculation is (1 + (0.037 / 2))2 – 1 = 3.73%.

With a Bond

Let’s now consider a bond issued by General Electric. As of March 2019, General Electric offers a noncallable semiannual coupon with a 4% coupon rate expiring Dec. 15, 2023. The nominal, or stated rate, of the bond, is 8%—or the 4% coupon rate times two annual coupons. However, the annual equivalent rate is higher, given the fact that interest is paid twice a year. The AER of the bond is calculated as (1+ (0.04 / 2 ))2 – 1 = 8.16%.

Annual Equivalent Rate vs. Stated Interest

While the stated interest rate doesn’t account for compounding, the AER does. The stated rate will generally be lower than AER if there’s more than one compounding period. AER is used to determine which banks offer better rates and which investments might be attractive.

Advantages and Disadvantages of the AER

The primary advantage of AER is that it is the real rate of interest because it accounts for the effects of compounding. In addition, it is an important tool for investors because it helps them evaluate bonds, loans, or accounts to understand their real return on investment (ROI).

Unfortunately, when investors are evaluating different investment options, the AER is usually not stated. Investors must do the work of calculating the figure themselves. It’s also important to keep in mind that AER doesn’t include any fees that might be tied to purchasing or selling the investment. Also, compounding itself has limitations, with the maximum possible rate being continuous compounding.

Pros of AER

  • Unlike the APR, AER reveals the actual interest rate

  • Crucial in finding the true ROI from interest-bearing assets. 

Cons of AER

  • Investors must do the work of calculating AER themselves

  • AER doesn’t take into account fees that may be incurred from the investment

  • Compounding has limitations, with the maximum possible rate being continuous compounding

Special Considerations

AER is one of the various ways to calculate interest on interest, which is called compounding. Compounding refers to earning or paying interest on previous interest, which is added to the principal sum of a deposit or loan. Compounding allows investors to boost their returns because they can accrue additional profit based on the interest they’ve already earned.

One of Warren Buffett’s famous quotes is, “My wealth has come from a combination of living in America, some lucky genes, and compound interest.” Albert Einstein reportedly referred to compound interest as mankind’s greatest invention. 

When you are borrowing money (in the form of loans), you want to minimize the effects of compounding. On the other hand, all investors want to maximize compounding on their investments. Many financial institutions will quote interest rates that use compounding principles to their advantage. As a consumer, it is important to understand AER so you can determine the interest rate you are really getting.

Where Can I Find an AER Calculator Online?

What Is a Nominal Interest Rate?

The nominal interest rate is the advertised or stated interest rate on a loan, without taking into account any fees or compounding of interest. The nominal interest rate is what is specified in the loan contract, without adjusting for compounding. Once the compounding adjustment has been made, this is the effective interest rate.

What Is a Real Interest Rate?

A real interest rate is an interest rate that has been adjusted to remove the effects of inflation. Real interest rates reflect the real cost of funds, in the case of a loan (and a borrower) and the real yield (or ROI) for an investor. The real interest rate of an investment is calculated as the difference between the nominal interest rate and the inflation rate.

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Annual General Meeting (AGM): Definition and Purpose

Written by admin. Posted in A, Financial Terms Dictionary

Annual General Meeting (AGM): Definition and Purpose

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What Is an Annual General Meeting (AGM)?

An annual general meeting (AGM) is a yearly gathering of a company’s interested shareholders. At an AGM, the directors of the company present an annual report containing information for shareholders about the company’s performance and strategy.

Shareholders with voting rights vote on current issues, such as appointments to the company’s board of directors, executive compensation, dividend payments, and the selection of auditors.

Key Takeaways

  • An annual general meeting (AGM) is the yearly gathering of a company’s interested shareholders.
  • At an annual general meeting (AGM), directors of the company present the company’s financial performance and shareholders vote on the issues at hand.
  • Shareholders who do not attend the meeting in person may usually vote by proxy, which can be done online or by mail.
  • At an AGM, there is often a time set aside for shareholders to ask questions to the directors of the company.
  • Activist shareholders may use an AGM as an opportunity to express their concerns.

Click Play to Learn What Annual General Meetings Are

How an Annual General Meeting (AGM) Works

An annual general meeting, or annual shareholder meeting, is primarily held to allow shareholders to vote on both company issues and the selection of the company’s board of directors. In large companies, this meeting is typically the only time during the year when shareholders and executives interact.

The exact rules governing an AGM vary according to jurisdiction. As outlined by many states in their laws of incorporation, both public and private companies must hold AGMs, though the rules tend to be more stringent for publicly traded companies.

Public companies must file annual proxy statements, known as Form DEF 14A, with the Securities and Exchange Commission (SEC). The filing will specify the date, time, and location of the annual meeting, as well as executive compensation and any material matters of the company concerning shareholder voting and nominated directors.

Annual general meetings (AGMs) are important for the transparency they provide, the ability to include shareholders, as well as bringing management to accountability.

Qualifications for an Annual General Meeting (AGM)

The corporate bylaws that govern a company, along with its jurisdiction, memorandum, and articles of association, contain the rules governing an AGM. For example, there are provisions detailing how far in advance shareholders must be notified of where and when an AGM will be held and how to vote by proxy. In most jurisdictions, the following items, by law, must be discussed at an AGM:

  • Minutes of the previous meeting: The minutes of the previous year’s AGM must be presented and approved.
  • Financial statements: The company presents its annual financial statements to its shareholders for approval.
  • Ratification of the director’s actions: The shareholders approve and ratify (or not) the decisions made by the board of directors over the previous year. This often includes the payment of a dividend.
  • Election of the board of directors: The shareholders elect the board of directors for the upcoming year.

Additional Topics Covered at an Annual General Meeting (AGM)

If the company has not been performing well, the AGM is also when shareholders can question the board of directors and management as to why performance has been poor. The shareholders can demand satisfactory answers as well as to inquire about the strategies that management plans to implement to turn the company around.

The AGM is also when shareholders can vote on company matters other than electing the board of directors. For example, if management is contemplating a merger or an acquisition, the proposal can be presented to the shareholders and they can vote on whether or not the company should proceed.

Several other elements may be added to an AGM agenda. Often, the company’s directors and executives use an AGM as their opportunity to share their vision of the company’s future with the shareholders. For example, at the AGM for Berkshire Hathaway, Warren Buffett delivers long speeches on his views of the company and the economy as a whole.

Berkshire Hathaway’s annual gathering has become so popular that it is attended by tens of thousands of people each year, and it’s been dubbed the “Woodstock for Capitalists.”

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