Amortization

Amortization is the gradual repayment of a loan through a series of scheduled payments, each of which covers the interest that has accrued on the outstanding balance since the previous payment and applies whatever is left over to reduce that balance. An amortization schedule is the table setting out that division for every payment across the life of the loan, from the first payment to the one that brings the balance to zero. A loan that repays itself completely by maturity is fully amortizing; one whose scheduled payments leave a balance behind is partially amortizing, and the remainder is a balloon payment.

The word carries two other meanings that have nothing to do with a payment schedule, and both appear often enough to cause confusion. In accounting, amortization is the systematic write-off of an intangible asset's cost over its useful life, which is the counterpart of depreciation for tangible assets and is why the three words travel together in the phrase "depreciation, depletion or amortization." And in the rules for taking penalty-free early withdrawals from a retirement account, one of the permitted calculations is called the fixed amortization method, which borrows the arithmetic without being about a loan at all. Neither is the subject here.

The mechanic is a consequence of arithmetic, not a policy choice, and knowing that removes most of the suspicion around it. Interest is charged on the amount currently owed. On a level-payment loan the payment is fixed, so the interest portion is whatever the balance requires this month and the principal portion is simply the remainder. As each payment reduces the balance, next month's interest charge is smaller, which leaves more of the same payment available for principal. The two portions therefore move in lockstep in opposite directions, and the amount by which the principal portion grows each month is exactly the amount by which the interest portion shrinks. Nobody decided that early payments would be mostly interest. It falls out of charging interest on a balance that starts at its maximum.

The consequence people find hardest to believe is about elapsed time. Because the principal portion starts small and grows slowly, progress against the balance is heavily back-loaded. On a thirty-year loan the halfway point in payments is nowhere near the halfway point in principal, and the payment at which the principal portion first exceeds the interest portion arrives much later than intuition suggests. There is a clean way to locate that crossover: it happens once the balance falls below half the payment divided by the monthly interest rate, because that is the balance at which the month's interest charge equals half the payment. The higher the rate, the later in the term the crossover falls.

Extra principal works through the balance, which is why timing decides its value. A dollar applied to principal removes every future interest charge that dollar would have generated for the rest of the loan, so the same extra dollar is worth far more in year two than in year twenty-five. That is also why an extra payment does not shorten a level-payment loan by shortening the payment: the payment stays the same and the schedule simply ends earlier, unless the lender agrees to recast it.

Precomputed interest is the exception where that reasoning fails, and it is worth identifying before signing anything. On a simple-interest loan, the common structure for mortgages and most auto loans today, interest accrues on the balance as it stands, so paying early reduces interest automatically. On a precomputed loan the whole finance charge is calculated at the outset and built into the amount owed, so paying early does not by itself stop anything accruing. Federal law supplies the remedy rather than banning the structure. 15 USC 1615(a)(1) provides that if a consumer prepays in full the financed amount under any consumer credit transaction, "the creditor shall promptly refund any unearned portion of the interest charge to the consumer," with a de minimis exception where the refund would be under $1. Subsection (a)(3) applies that regardless of the manner or reason for the prepayment, expressly including a prepayment made in connection with a refinancing, consolidation or restructuring, and one arising from the creditor accelerating the debt.

How the refund is computed is where the older abuse lived. 15 USC 1615(b) requires that for a precomputed consumer credit transaction with a term exceeding 61 months, consummated after 30 September 1993, the refund be computed "based on a method which is at least as favorable to the consumer as the actuarial method." That is the provision that displaced the Rule of 78s, a front-loading refund formula, and the length condition is doing real work: the federal requirement reaches loans longer than 61 months, which leaves shorter precomputed loans outside it. Subsection (c) adds a useful right: on request, the creditor must supply a statement of the amount needed to prepay in full and the amount of any refund included in it, within five days, and one such statement a year is free.

Negative amortization, stated carefully, because both of the common descriptions of it are wrong. Negative amortization occurs when a scheduled payment is smaller than the interest accruing, so the shortfall is added to the balance and the debt grows while payments are being made. It is not prohibited in general. Regulation Z at 12 CFR 1026.19(b)(2)(vii) still requires any negative-amortization feature to be disclosed in the loan program disclosure for an adjustable-rate mortgage, and the statutory prohibition at 15 USC 1639(f) reaches high-cost mortgages rather than all loans. What is true is that a borrower will not meet it in a mainstream loan today, and the reason is a definition rather than a ban: 12 CFR 1026.43(e)(2)(i) requires a qualified mortgage's regular periodic payments not to "result in an increase of the principal balance," not to allow deferral of principal, and not to result in a balloon payment, with the term capped at 30 years by (e)(2)(ii). Lenders overwhelmingly originate qualified mortgages, so the feature has largely left the market through that route. Read the disclosure rather than assuming either way. On a credit card the same arithmetic has its own disclosure: where the minimum payment produces negative or no amortization, Regulation Z substitutes wording telling the cardholder the balance will never be paid off.

One interaction catches people who prepay a mortgage. Automatic termination of private mortgage insurance is keyed to the initial amortization schedule and applies irrespective of the outstanding balance, so extra principal does nothing to accelerate it. The separate route, a borrower request once the balance reaches 80% of original value, can be reached earlier through actual payments. So prepaying helps with one of the two mechanisms and not the other, which is worth knowing before treating extra principal as a way to get rid of the premium.

The level payment on a fully amortizing loan is set so that the schedule ends at exactly zero. It is the principal multiplied by the periodic rate and divided by one minus the quantity one plus the periodic rate raised to the power of minus the number of payments. From there each payment is split by charging the periodic rate against the current balance and applying whatever remains to principal.

A hypothetical example, using illustrative figures rather than any current market rate. A $250,000 loan at 6% a year for 30 years has a monthly rate of 0.5% (6% ÷ 12) and 360 payments, which produces a payment of $1,498.88.

Payment 1. Interest is $1,250.00 ($250,000 × 0.005). Principal is $248.88 ($1,498.88 − $1,250.00), so 83.4% of the first payment is interest ($1,250.00 ÷ $1,498.88). The balance falls to $249,751.12.

Payment 2. Interest is $1,248.76 ($249,751.12 × 0.005). Principal is $250.12 ($1,498.88 − $1,248.76). Notice the symmetry that is the whole mechanic: interest fell by $1.24 and principal rose by $1.24. That gap widens every month, slowly at first and then quickly.

Where the crossover sits. The principal portion first exceeds the interest portion once the month's interest charge falls below half the payment, which happens when the balance drops below $149,888 ($749.44 ÷ 0.005). On this loan that arrives a little past the eighteen-year mark, not at year fifteen.

What half the term actually buys. After 180 payments, about $177,600 of the original $250,000 is still outstanding, so roughly 29% of the principal has been retired after half the payments have been made. Over the full term the payments total about $539,600 ($1,498.88 × 360), of which about $289,600 is interest and $250,000 is the amount borrowed.

Pros

• A level payment is predictable, which is what makes a long-term loan budgetable at all.
• The schedule is fully determined at the outset, so the entire interest cost is knowable before signing.
• Interest is charged on the balance, so every extra dollar of principal permanently removes the interest it would have generated.
• The loan retires itself with no lump sum at the end, unlike a partially amortizing structure.

Cons

• Interest is front-loaded as an arithmetic consequence, so early years build very little equity.
• The crossover to a mostly-principal payment arrives later than most borrowers expect, and later still at higher rates.
• Extra principal shortens the schedule rather than reducing the payment, unless the lender agrees to recast it.
• On a precomputed loan paying early does not automatically save interest, and the refund method for shorter precomputed loans is not governed by the federal actuarial-method requirement.
• Extra principal does nothing to accelerate the automatic termination of private mortgage insurance, which follows the original schedule regardless of balance.