Amortization in lending refers to the process of spreading loan payments over time so that the debt is fully repaid by the end of the term. An amortized loan is one whose equal periodic payments cover both principal and interest, leaving a zero balance at maturity. The standard formula for the fixed monthly payment on a fully amortizing loan is \[M = P \cdot \frac{r(1+r)^n}{(1+r)^n - 1}\] where \(M\) is the monthly payment, \(P\) is the loan principal, \(r\) is the monthly interest rate (annual rate divided by 12), and \(n\) is the total number of payments. This expression, sometimes called the PMT function on financial calculators, is the foundation of every standard mortgage payment and most consumer installment loans.
An amortization schedule breaks each payment into its interest and principal portions and tracks the declining balance over time. To build one by hand, you calculate the interest charge as the beginning balance multiplied by the periodic rate, subtract that interest from the fixed payment to determine the principal portion, and then subtract the principal from the balance to obtain the new balance. Repeat this process until the balance reaches zero. Early rows show mostly interest because the balance is largest at the start; later rows show increasingly more principal. The crossover point, the month when the principal portion first exceeds the interest portion, occurs roughly between years 15 and 20 on a 30-year fixed mortgage, after which equity builds much faster.
Several variations depart from the standard front-loaded amortization pattern. Simple interest loans calculate interest each period on the current outstanding, declining balance, so paying off early yields substantial interest savings. Precomputed interest loans calculate the total interest upfront at origination and bake it into the schedule, so early payoff yields little savings. Straight-line amortization divides total interest evenly across all periods rather than front-loading it, and is uncommon in mortgages but used in some consumer and business installment loans. The Rule of 78 is a method of allocating interest in which each month's interest share is proportional to its month number, so early payments carry disproportionately more interest. Day count conventions such as 30/360 (assuming every month has 30 days) or actual/365 also affect the precise interest accrued, though over a full year 30/360 charges essentially the same as actual/365; it is actual/360, which charges actual days at a rate divided by 360, that genuinely raises the effective rate.
Payment frequency and extra payments also change the economics of amortization. Paying half the monthly amount every two weeks produces 26 half-payments, or 13 full payments, per year instead of 12, which shortens a 30-year loan by roughly 4 to 6 years. Extra principal payments, sometimes called curtailments, reduce the balance immediately, lowering the interest charged in every subsequent period and saving thousands of dollars over the loan's life. Even small additional amounts applied early in the loan's life can shave years off the term. Together, these techniques allow borrowers to manipulate the standard amortization schedule to pay off debt faster and reduce total interest, sometimes dramatically.