Amortization : Formula & Calculation

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 spreading out of 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 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. Amortization schedules begin with the outstanding loan balance. To arrive at the amount of monthly payments, the interest payment is calculated by multiplying the interest rate by the outstanding loan balance and dividing by 12. The amount of principal due in a given month is the total monthly payment (a flat amount) minus the interest payment for that month.

For the next month, the outstanding loan balance is calculated as the previous month’s outstanding balance minus the most recent principal payment. The interest payment is once again calculated off the new outstanding balance, and the pattern continues until all principal payments have been made, and the loan balance is zero at the end of the loan term.

Amortization Calculation

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

Principal Payment = TMP − ( OLB × Interest Rate 12 Months ) where: TMP = Total monthly payment OLB = Outstanding loan balance \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:

Total Payment = Loan Amount × [ ( i × 1 + i n 1 + i n ) − 1 ] where: i = Monthly interest rate n = Number of payments \begin{aligned}&\text{Total Payment} = \text{Loan Amount} \times \Bigg [ \Bigg ( \frac { i \times \frac { 1 + i }{ n } }{ \frac { 1 + i }{ n } } \Bigg ) - 1 \Bigg ] \\&\textbf{where:} \\&i = \text{Monthly interest rate} \\&n = \text{Number of payments} \\\end{aligned} Total Payment=Loan Amount×[(n1+ii×n1+i)−1]where:i=Monthly interest raten=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 0.0025% (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).

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 0.0025% (0.03 annual interest rate ÷ 12 months).

You 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).

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.

Amortizing intangible assets is important because it can reduce a business’ taxable income, and therefore its tax liability, while giving investors a better understanding of the company’s true earnings.

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 thusly:

$ 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

Total Payment Due

Computed Interest Due

Principal Due

Principal Balance

What Is Amortization?

The term “amortization” has two important meanings in finance. First, it can refer to the schedule of payments whereby a loan is paid off gradually over time, such as in the case of a mortgage or car loan. Second, it can refer to the practice of expensing the cost of an intangible asset over time.

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. Amortizing intangible assets is also important because it can reduce a business’ taxable income and therefore its tax liability, while giving investors a better understanding of the company’s true earnings.

What Is the Difference Between Amortization and 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.