Amortization

The systematic repayment or cost allocation of a loan or intangible asset over time.

Amortization means spreading a cost or repayment over time according to a schedule. In economics and finance, the word is used mainly in two ways: paying down a loan through regular installments, and allocating the cost of an intangible asset across its useful life.

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Loan Amortization

For a fully amortizing loan, each payment includes interest plus some principal. Early payments contain more interest because interest is charged on a larger outstanding balance. Later payments contain more principal because the remaining balance is smaller.

For principal P, periodic interest rate r, and n equal payments, the fixed payment is:

[ \text{Payment} = P\frac{r(1+r)^n}{(1+r)^n - 1} ]

This formula matters because it links loan size, maturity, and interest rate to the borrower’s cash-flow burden.

Asset Amortization

In accounting, amortization also means expensing the cost of an intangible asset such as a patent, license, or software asset over the period in which it is expected to generate benefits. That keeps reported cost aligned more closely with the revenue or service flow produced by the asset.

Why It Matters Economically

Amortization affects household budgets, firm cash flow, and valuation. Faster loan amortization reduces credit risk because the outstanding balance falls more quickly. On the accounting side, amortization changes measured profit over time even when cash payments happened earlier.

Knowledge Check

### What does amortization usually mean for a loan? - [x] Repaying principal and interest over time through scheduled payments - [ ] Paying only interest forever - [ ] Recording a one-time write-off with no schedule - [ ] Pricing a bond with no maturity date > **Explanation:** Loan amortization is a repayment pattern in which each scheduled payment reduces the outstanding balance. ### Why does the principal share of a fixed mortgage payment usually rise over time? - [ ] Because lenders raise the interest rate every period - [x] Because interest is charged on a declining outstanding balance - [ ] Because the loan becomes interest-only near maturity - [ ] Because inflation removes principal automatically > **Explanation:** As the balance falls, the interest portion shrinks, so more of each fixed payment goes to principal. ### How is accounting amortization different from loan amortization? - [ ] It always refers to tax credits only - [x] It allocates the cost of an intangible asset instead of repaying borrowed principal - [ ] It ignores time completely - [ ] It applies only to labor contracts > **Explanation:** In accounting, amortization is a cost-allocation method for intangibles rather than a debt repayment schedule.