Amortization Examples: Loan and Asset Calculations
Understand how amortization works to spread costs over time. This guide provides clear calculation examples for both personal debt and business assets.
Amortization is a financial process of paying down a debt with regular payments over a set period. For loans like a mortgage or auto loan, each payment is divided into two parts. A portion covers the interest charged by the lender, while the rest reduces the original loan balance.
In business, amortization applies to intangible assets, which are valuable items without physical substance, like patents or copyrights. Instead of a single expense, the acquisition cost is gradually charged as an expense over the asset’s useful life. This accounting practice matches the asset’s cost to the revenue it helps generate, providing a more accurate picture of company profitability.
Components of an Amortization Calculation
The calculations for loan amortization apply to installment loans and are based on three components established in the loan agreement.
The first component is the principal, the total sum of money borrowed. For example, if you take out a $30,000 car loan, the principal is $30,000. This is the core amount that must be repaid, separate from any borrowing costs.
Another component is the interest rate, representing the cost of borrowing as a percentage. Interest rates are quoted as an annual percentage rate (APR). For amortization calculations, this rate is applied to the outstanding loan balance each payment period.
The final piece is the loan term, the total time allotted to repay the loan. Common terms for auto loans are five years (60 months), while mortgages often have terms of 15 or 30 years. A longer term results in lower monthly payments but increases the total interest paid over the life of the loan.
Loan Amortization Example
Consider a fixed-rate auto loan with a $40,000 principal, a 6% annual interest rate, and a five-year term. These values are used to calculate the fixed monthly payment.
The formula for the monthly payment (M) is M = P [i(1 + i)^n] / [(1 + i)^n – 1]. Here, ‘P’ is the principal ($40,000), ‘i’ is the monthly interest rate, and ‘n’ is the number of payments. The 6% annual rate is divided by 12 to get a 0.5% (0.005) monthly rate, and the five-year term becomes 60 months for ‘n’. Plugging these values in results in a monthly payment of approximately $773.
The first $773 payment illustrates how amortization works. The interest for the first month is calculated by multiplying the principal ($40,000) by the monthly interest rate (0.005), which equals $200. The remaining $573 is applied to the principal, reducing the loan balance to $39,427.
For the second payment, interest is calculated on the new balance of $39,427. This results in an interest payment of about $197.14. Because the monthly payment is fixed at $773, the principal portion increases to $575.86. This pattern continues, with the interest portion of each payment decreasing while the principal portion increases.
An amortization schedule tables these payments over the loan term. For this $40,000 loan, the principal balance is reduced to approximately $33,033 by the end of the first year (payment 12). By the end of the third year (payment 36), the balance is down to around $16,958, with a larger portion of each payment going toward principal.
Intangible Asset Amortization Example
In business accounting, amortization is used to expense the cost of intangible assets over their useful life. An intangible asset is a non-physical item with value, such as a patent, trademark, or copyright. This process is an accounting entry, not a cash payment, that affects a company’s financial statements.
The most common approach is the straight-line method. For example, a tech company acquires a patent for $100,000 and determines it has a useful life of 10 years. After 10 years, the technology will be obsolete, and the patent will have no residual value.
The annual amortization expense is calculated by dividing the asset’s cost ($100,000) by its useful life (10 years), resulting in a $10,000 expense. This amount is recorded annually on the company’s income statement as a non-cash expense. This reduces the company’s reported taxable income.
This expense is also recorded on the balance sheet. The patent’s value, initially $100,000, is reduced by the accumulated amortization each year. After the first year, its book value is $90,000, then $80,000 the next, until it reaches zero at the end of the tenth year.