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What Is an Amortization Schedule? How to Calculate with Formula

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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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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​)n−1where: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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What Is Adjusted Gross Income (AGI)?

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What Is Adjusted Gross Income (AGI)?

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What Is Adjusted Gross Income (AGI)?

Adjusted gross income (AGI) is the figure that the Internal Revenue Service (IRS) uses to determine your income tax liability for the year. It is calculated by subtracting certain adjustments from gross income, such as business expenses, student loan interest payments, and other expenses. After calculating a taxpayer’s AGI, the next step is to subtract deductions to determine their taxable income.

The IRS also uses other income metrics, such as modified AGI (MAGI), for specific programs and retirement accounts.

Key Takeaways

  • The IRS uses your adjusted gross income (AGI) to determine how much income tax you owe for the year.
  • AGI is calculated by taking all of your income for the year (your gross income) and subtracting certain adjustments to income.
  • Your AGI can affect the size of your tax deductions as well as your eligibility for some types of retirement plan contributions, such as a Roth individual retirement account (Roth IRA).
  • Modified adjusted gross income (MAGI) is your AGI with some otherwise-allowable deductions added back in. For many people, AGI and MAGI will be the same.
  • Among the items subtracted from your gross income when calculating your AGI are alimony payments and educator expenses.

Click Play to Learn All About Adjusted Gross Income

Understanding Adjusted Gross Income (AGI)

As prescribed in the United States tax code, AGI is a modification of gross income. Gross income is simply the sum of all the money you earned in a year, which may include wages, dividends, capital gains, interest income, royalties, rental income, alimony, and retirement distributions, before tax or other deductions. AGI makes certain adjustments to your gross income to reach the figure on which your tax liability will be calculated.

Many U.S. states also use the AGI from federal returns to calculate how much individuals owe in state income taxes. States may modify this number further with state-specific deductions and credits.

AGI is an important figure because it is what is used to determine your eligibility for certain deductions and credits.

Common Adjustments

The items subtracted from your gross income to calculate your AGI are referred to as adjustments to income, and you report them on Schedule 1 of your tax return when you file your annual tax return. Some of the most common adjustments are listed here, along with the separate tax forms on which a few of them are calculated:

  • Alimony payments (for divorces filed before Jan. 1, 2019)
  • Early withdrawal penalties on savings
  • Educator expenses
  • Employee business expenses for armed forces reservists, qualified performing artists, fee-basis state or local government officials, and employees with impairment-related work expenses (Form 2106)
  • Health Savings Account (HSA) deductions (Form 8889)
  • Moving expenses for members of the armed forces (Form 3903)
  • Self-employed Simplified Employee Pension (SEP), Savings Incentive Match Plan for Employees of Small Employers (SIMPLE), and qualified plans
  • Self-employed health insurance deduction
  • Self-employment tax (the deductible portion)
  • Student loan interest deduction

How to Calculate Adjusted Gross Income

If you use software to prepare your tax return, it will calculate your AGI once you input your numbers. If you calculate it yourself, you’ll begin by tallying your reported income for the year. That might include job income, as reported to the IRS by your employer on a W-2 form, plus other income, such as dividends and miscellaneous income, reported on 1099 forms.

Next, you add any taxable income from other sources, such as profit on the sale of a property, unemployment compensation, pensions, Social Security payments, or anything else that hasn’t already been reported to the IRS. Many of these income items are also listed on IRS Schedule 1.

The next step is to subtract the applicable adjustments to the income listed above from your reported income. The resulting figure is your AGI. To determine your taxable income, subtract either the standard deduction or your total itemized deductions from your AGI. In most cases, you can choose whichever gives you the most benefit.

For example, the standard deduction for tax returns for married couples filing jointly was $25,900 in 2022, rising to $27,700 in 2023, so couples whose itemized deductions exceed that amount would generally opt to itemize, while others would take the standard deduction.

The IRS provides a list of itemized deductions and the requirements for claiming them on its website. Your AGI also affects your eligibility for many of the deductions and credits available on your tax return. In general, the lower your AGI, the more significant the number of deductions and credits you will be eligible to claim, and the more you’ll be able to reduce your tax bill.

An Example of AGI Affecting Deductions

Let’s say you had some significant dental expenses during the year that weren’t reimbursed by insurance, and you’ve decided to itemize your deductions. You are allowed to deduct the portion of those expenses that exceed 7.5% of your AGI.

This means that if you report $12,000 in unreimbursed dental expenses and have an AGI of $100,000, you can deduct the amount that exceeds $7,500, which is $4,500. However, if your AGI is $50,000, the 7.5% reduction is just $3,750, and you’d be entitled to deduct a larger amount of that $12,000, in this case $8,250.

Adjusted Gross Income (AGI) vs. Modified Adjusted Gross Income (MAGI)

In addition to AGI, some tax calculations and government programs call for using what’s known as your modified adjusted gross income, or MAGI. This figure starts with your AGI, then adds back certain items, such as any deductions you take for student loan interest or tuition and fees.

Your MAGI is used to determine how much, if anything, you can contribute to a Roth individual retirement account (Roth IRA) in any given year. It is also used to calculate your income if you apply for Marketplace health insurance under the Affordable Care Act (ACA).

Many people with relatively uncomplicated financial lives find that their AGI and MAGI are the same number or very close.

If you file your taxes electronically, the IRS form will ask you for your previous year’s AGI as a way of verifying your identity.

Adjusted Gross Income vs. Gross Income vs. Taxable Income

Your gross income is all of the money you’ve earned in a year that isn’t exempt from taxation. This can be in the form of salary, wages, interest, dividends, capital gains, and so on.

Your adjusted gross income takes that amount and takes out certain qualified expenses and adjustments.

Taxpayers can then take either the standard deduction for their filing status or itemize the deductible expenses they paid during the year. You’re not permitted to both itemize deductions and claim the standard deduction. The result is your taxable income.

Where to Find Your Adjusted Gross Income (AGI)

You report your AGI on line 11 of IRS Form 1040, which is the form you use to file your income taxes for the year. Keep that number handy after completing your taxes, because you will need it again if you e-file your taxes next year. The IRS uses it as a way to verify your identity.

Also, note that as of January 2022, almost anyone may use the IRS Free File program to file their federal (and, in some cases, state) taxes electronically at no charge.

Frequently Asked Questions

What Does Adjusted Gross Income (AGI) Mean for Tax Payments?

Adjusted gross income (AGI) is essentially your income for the year after accounting for all applicable tax deductions. It is an important number that is used by the Internal Revenue Service (IRS) to determine how much you owe in taxes. AGI is calculated by taking your gross income from the year and subtracting any deductions that you are eligible to claim. Therefore, your AGI will always be less than or equal to your gross income.

What Are Some Common Adjustments Used When Determining AGI?

There are a wide variety of adjustments that might be made when calculating AGI, depending on the financial and life circumstances of the filer. Moreover, since the tax laws can be changed by lawmakers, the list of available adjustments can change over time. Some of the most common adjustments used when calculating AGI include reductions for alimony and student loan interest payments.

What Is the Difference Between AGI and Modified Adjusted Gross Income (MAGI)?

AGI and modified adjusted gross income (MAGI) are very similar, except that MAGI adds back certain deductions. For this reason, MAGI would always be larger than or equal to AGI. Common examples of deductions that are added back to calculate MAGI include foreign earned income, income earned on U.S. savings bonds, and losses arising from a publicly traded partnership.

The Bottom Line

Adjusted gross income, or AGI, is your gross income after it has been adjusted for certain qualified deductions that are permitted by the Internal Revenue Service (IRS). These qualified deductions reduce an individual’s gross income, thus reducing the taxable income that they will ultimately have to pay taxes on. You can save money come tax season by lowering your AGI, which will lower your taxable income, in turn. However, many of the adjustments allowed for AGI are specific for particular circumstances that may not apply to everyone.

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Advance/Decline (A/D) Line: Definition and What It Tells You

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Advance/Decline (A/D) Line: Definition and What It Tells You

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What Is the Advance/Decline (A/D) Line?

The advance/decline line (or A/D line) is a technical indicator that plots the difference between the number of advancing and declining stocks on a daily basis. The indicator is cumulative, with a positive number being added to the prior number, or if the number is negative it is subtracted from the prior number.

The A/D line is used to show market sentiment, as it tells traders whether there are more stocks rising or falling. It is used to confirm price trends in major indexes, and can also warn of reversals when divergence occurs.

TradingView.

Key Takeaways

  • The advance/decline (A/D) line is a breadth indicator used to show how many stocks are participating in a stock market rally or decline.
  • When major indexes are rallying, a rising A/D line confirms the uptrend showing strong participation.
  • If major indexes are rallying and the A/D line is falling, it shows that fewer stocks are participating in the rally which means the index could be nearing the end of its rally.
  • When major indexes are declining, a falling advance/decline line confirms the downtrend.
  • If major indexes are declining and the A/D line is rising, fewer stocks are declining over time, which means the index may be near the end of its decline.

The Formula for Advance/Decline (A/D) Line Is:


A/D = Net Advances + { PA, if PA value exists 0, if no PA value where: Net Advances = Difference between number of daily ascending and declining stocks PA = Previous Advances Previous Advances = Prior indicator reading \begin{aligned} &\text{A/D} = \text{Net Advances} + \begin{cases} \text{PA, if PA value exists} \\ \text{0, if no PA value} \\ \end{cases} \\ &\textbf{where:} \\ &\text{Net Advances} = \text{Difference between number of daily} \\ &\text{ascending and declining stocks} \\ &\text{PA} = \text{Previous Advances} \\ &\text{Previous Advances} = \text{Prior indicator reading} \\ \end{aligned} ​A/D=Net Advances+{PA, if PA value exists0, if no PA value​where:Net Advances=Difference between number of dailyascending and declining stocksPA=Previous AdvancesPrevious Advances=Prior indicator reading​

How to Calculate the A/D Line

  1. Subtract the number of stocks that finished lower on the day from the number of stocks that finished higher on the day. This will give you the Net Advances.
  2. If this is the first time calculating the average, the Net Advances will be the first value used for the indicator.
  3. On the next day, calculate the Net Advances for that day. Add to the total from the prior day if positive or subtract if negative.
  4. Repeat steps one and three daily.

What Does the A/D Line Tell You?

The A/D line is used to confirm the strength of a current trend and its likelihood of reversing. The indicator shows if the majority of stocks are participating in the direction of the market. 

If the indexes are moving up but the A/D line is sloping downwards, called bearish divergence, it’s a sign that the markets are losing their breadth and may be about to reverse direction. If the slope of the A/D line is up and the market is trending upward, then the market is said to be healthy.

Conversely, if the indexes are continuing to move lower and the A/D line has turned upwards, called bullish divergence, it may be an indication that the sellers are losing their conviction. If the A/D line and the markets are both trending lower together, there is a greater chance that declining prices will continue.

Difference Between the A/D Line and Arms Index (TRIN)

The A/D line is typically used as a longer-term indicator, showing how many stocks are rising and falling over time. The Arms Index (TRIN), on the other hand, is typically a shorter-term indicator that measures the ratio of advancing stocks to the ratio of advancing volume. Because the calculations and the time frame they focus on are different, both these indicators tell traders different pieces of information.

Limitations of Using the A/D Line

The A/D line won’t always provide accurate readings in regards to NASDAQ stocks. This is because the NASDAQ frequently lists small speculative companies, many of which eventually fail or get delisted. While the stocks get delisted on the exchange, they remain in the prior calculated values of the A/D line. This then affects future calculations which are added to the cumulative prior value. Because of this, the A/D line will sometimes fall for extended periods of time, even while NASDAQ-related indexes are rising.

Another thing to be aware of is that some indexes are market capitalization weighted. This means that the bigger the company the more impact they have on the index’s movement. The A/D line gives equal weight to all stocks. Therefore, it is a better gauge of the average small to mid-cap stock, and not the fewer in number large or mega-cap stocks.

Investopedia does not provide tax, investment, or financial services and advice. The information is presented without consideration of the investment objectives, risk tolerance, or financial circumstances of any specific investor and might not be suitable for all investors. Investing involves risk, including the possible loss of principal.

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