What Is an Amortization Schedule? How to Calculate with Formula

What Is Amortization?

Amortization is an accounting technique used to periodically lower the book value of a loan or an intangible asset over a set period of time. Concerning a loan, amortization focuses on spreading out loan payments over time. When applied to an asset, amortization is similar to depreciation.

Understanding Amortization

The term “amortization” refers to two situations. First, amortization is used in the process of paying off debt through regular principal and interest payments over time. An amortization schedule is used to reduce the current balance on a loan—for example, a mortgage or a car loan—through installment payments.

Second, amortization can also refer to the practice of spreading out capital expenses related to intangible assets over a specific duration—usually over the asset’s useful life—for accounting and tax purposes.

Amortization of Loans

Amortization can refer to the process of paying off debt over time in regular installments of interest and principal sufficient to repay the loan in full by its maturity date.

A loan amortization schedule represents the complete table of periodic loan payments, showing the amount of principal and interest that comprise each level payment until the loan is paid off at the end of its term. A higher percentage of the flat monthly payment goes toward interest early in the loan, but with each subsequent payment, a greater percentage of it goes toward the loan’s principal.

Amortization can be calculated using most modern financial calculators, spreadsheet software packages (such as Microsoft Excel), or online amortization calculators. When entering into a loan agreement, the lender may provide a copy of the amortization schedule (or at least have identified the term of the loan in which payments must be made).

Amortization schedules can be customized based on your loan and your personal circumstances. With more sophisticated amortization calculators you can compare how making accelerated payments can accelerate your amortization. If for example, you are expecting an inheritance or you get a set yearly bonus, you can use these tools to compare how applying that windfall to your debt can affect your loan's maturity date and your interest cost over the life of the loan.

How to calculate loan amortization

The formula to calculate the monthly principal due on an amortized loan is as follows:

$\begin{aligned}&\text{Principal Payment} = \text{TMP} - \Big ( \text{OLB} \times \frac { \text{Interest Rate} }{ \text{12 Months} } \Big ) \\&\textbf{where:} \\&\text{TMP} = \text{Total monthly payment} \\&\text{OLB} = \text{Outstanding loan balance} \\\end{aligned}$​Principal Payment=TMP−(OLB×12 MonthsInterest Rate​)where:TMP=Total monthly paymentOLB=Outstanding loan balance​

Typically, the total monthly payment is specified when you take out a loan. However, if you are attempting to estimate or compare monthly payments based on a given set of factors, such as loan amount and interest rate, then you may need to calculate the monthly payment as well. If you need to calculate the total monthly payment for any reason, the formula is as follows:

$\begin{aligned}&\text{Total Payment} = \text{Loan Amount} \times \Bigg [ \frac { i \times (1 + i) ^n }{ (1 + i)^n - 1 } \Bigg ] \\&\textbf{where:} \\&i = \text{Monthly interest payment} \\&n = \text{Number of payments} \\\end{aligned}$​Total Payment=Loan Amount×[(1+i)n−1i×(1+i)n​]where:i=Monthly interest paymentn=Number of payments​

You’ll need to divide your annual interest rate by 12. For example, if your annual interest rate is 3%, then your monthly interest rate will be 0.25% (0.03 annual interest rate ÷ 12 months). You'll also multiply the number of years in your loan term by 12. For example, a four-year car loan would have 48 payments (four years × 12 months).

Preparing amortization schedules

Amortization schedules usually have six columns, each communicating information to the borrower and lender. The six columns are often laid out as shown below:

• 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 the 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.

Pros and Cons of Loan Amortization

Amortized loans feature a level payment over their lives, which helps individuals budget their cash flows over the long term. Amortized loans are also beneficial in that there is always a principal component in each payment, so that the outstanding balance of the loan is reduced incrementally over time.

The main drawback of amortized loans is that relatively little principal is paid off in the early stages of the loan, with most of each payment going toward interest. This means that for a mortgage, for example, very little equity is being built up early on, which is unhelpful if you want to sell a home after just a few years.

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.

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 concerning the portion of a loan payment that consists of interest versus the portion that is principal. This can be useful for purposes such as deducting interest payments on income tax forms. It is also useful for planning to understand what a company's future debt balance will be 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 of fixed assets remains on a company's books; however, the company also reports this contra asset amount as a net reduced book value amount.

Finally, 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:

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

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

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

The remaining $589.03 goes toward principal.

$\begin{aligned}&\$664.03 \ \text{total monthly payment} - \$75 \ \text{interest payment} \\ \end{aligned}$​$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.

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.