Amortization Calculator

What a loan amortization table displays

Amortization is the process of paying off a sum you borrowed with equal installments on a fixed schedule. Each payment includes the interest that built up since the last one, and whatever is left over reduces the balance. A loan amortization table lists that split for every payment: the sum, the interest part, the principal part, and what remains.

Two results follow from that order. Interest is charged on the balance, so a large balance produces a large interest charge. Principal is whatever survives after the interest is paid, so early payments barely move the balance. On a 30 year mortgage at 6.5 percent, the payment is 1,580.17, and 1,354.17 of the first one is interest. Only 226.00 touches the loan.

This calculator builds the entire schedule from three fields: the sum borrowed, the annual interest rate, and the term in years or months. A fourth, optional field contributes extra principal each month and displays how many payments disappear and how much interest that avoids.

Amortization applies to any fixed rate installment loan: a mortgage, a car loan, a personal loan, a student loan. Credit cards sit outside it because the payment changes with the balance and there is no agreed payoff date.

The payment formula, term by term

The monthly payment is built from P x r x (1 + r)^n / ((1 + r)^n - 1). P is the sum borrowed, r is the annual rate divided by 12, and n is how many monthly payments you make. The formula returns the payment that clears both interest and principal precisely at the last payment.

For 250,000 at 6.5 percent over 30 years, r is 0.0054167 and n is 360. The growth factor (1 + r)^n equals 6.9918, so the fraction is 6.9918 / 5.9918. Multiply by the balance and the monthly rate, and the payment is 1,580.17.

A quick test with the first month: 250,000 x 0.0054167 = 1,354.17 of interest. Subtract that from 1,580.17 and 226.00 is left for principal. The next month begins at 249,774.00, so the interest charge drops by about a dollar and the principal part climbs by the same margin.

At a zero rate the formula collapses to P / n, which is why a 0 percent auto note is just the sticker amount divided by the length in months. At any positive rate the check is bigger than that flat split, and the difference is the expense of borrowing. The same formula runs backward from a payment to a balance, which is how affordability tools work.

The exponent is the step that trips people up. A spreadsheet or a desk calculator manages it, and the order of operations counts: divide before you subtract in the denominator.

A 30 year example, payment by payment

The rows below come from the schedule for a 250,000 loan at 6.5 percent. Every row has the same payment. What changes is the split between interest and principal.

Month 1 sends 1,354.17 to interest and 226.00 to principal. By month 120 the interest part is 1,150.34 and the principal part 429.83. At month 240 the split is close to even: 758.25 of interest and 821.92 of principal. The last payment carries 8.51 of interest and 1,571.66 of principal.

Tally the interest and it totals 318,861.22. The payments total 568,861.22, so interest alone equals 127.5 percent of the sum borrowed. Principal finally exceeds interest around payment 233, which is past the 19 year mark. For most of the loan, the bigger share of each check went to the issuer.

What the balance does along the way

A single payment tells you little. The balance over time tells you how much of the loan is already behind you.

One year of payments costs 18,962.04 and reduces the balance by 2,794.31. The other 16,167.73 is interest. At the 15 year mark, half the calendar has passed but only 27.4 percent of the principal is gone. At 20 years it is 44.3 percent. The curve is steep only near the end.

The first five years carry 78,837.65 of interest, 24.7 percent of the lifetime total. That front loading explains two common results: refinancing late in a loan saves little, and extra payments made early save far more than the same dollars sent in year 25.

Escrow is the piece people mix up with amortization. An escrow or impound fund gathers a share of the property tax and homeowners coverage with each check, holds it, and pays the bill when it is due. Those funds never touch the principal, so they cannot trim the term. It only changes the size of the check. A 1,800 dollar tax bill puts 150 a month into escrow and nothing toward principal.

Extra principal: what 200 dollars a month changes

Extra funds go straight to principal, so they clear that principal and every later interest charge on it. The table compares four monthly habits on the same 250,000 loan.

With 200 extra, the loan finishes at payment 265, which is 22 years and 1 month instead of 30, and the final payment drops to 1,278.21 because the balance runs out mid payment. Interest drops to 221,243.10, a saving of 97,618.12.

With 100 extra the saving is 58,859.89 and the payoff shifts to payment 304. With 500 extra it shifts to payment 195 and saves 163,515.95. The first hundred dollars saves more than the second, because it arrives earlier and has more months of interest to prevent.

One dollar of extra principal in month one avoids about 5.99 dollars of interest over the full term, since the funds would otherwise sit on the balance for 360 months at 0.5417 percent a month. That is why a small early habit beats a large late one.

Ask the servicer to apply extra funds to principal and verify it in a written note. Some agreements treat it as an early installment, which postpones the next due date instead of trimming the term.

Two variations are useful. A recast uses a lump sum and re-spreads the remaining balance across the existing term, which lowers the monthly check instead of ending the loan early. Servicers frequently charge a small fee and set a minimum. A biweekly arrangement collects half the check every two weeks, which yields 26 half payments, or 13 full ones, each year; that extra payment does the same work as adding one twelfth to every check, commonly with no setup fee.

Rate and term: the two dials that set total interest

Two settings decide the cost, and they pull in opposite directions on the monthly payment.

At the same 6.5 percent, a 15 year term lifts the payment by 597.60 and trims interest to 141,998.31. That is 176,862.91 less interest over the life of the loan, in exchange for seven and a half years of higher payments.

The rate shifts the answer just as hard. One point higher on the 30 year loan contributes 167.87 to the payment and 60,431.84 to total interest. A point below trims the payment to 1,419.47 and interest to 261,010.10. A homeowner who accepts the 7.5 percent rate pays 60,431.84 more than one who qualifies for 6.5 percent on the same house.

Both dials attack the same target: the balance that interest is charged on. A briefer term clears that balance faster. A cheaper rate charges less for it. Doing both is how a loan gets cheap, and doing neither is how a 30 year loan winds up costing more than the house.

Rate buydowns are another lever. Paying discount fees at closing lowers the rate, either for the full term or for a set stretch. One point commonly costs one percent of the loan amount, or 2,500 here, and may trim the rate by a quarter point. The breakeven month is when the smaller check has repaid that upfront cost. On a long hold it can pay off; on a brief one it rarely does.

Car loans, credit cards and mortgages side by side

The math is the same, but the clocks are different. A mortgage runs for decades, a vehicle loan for a few years, and a credit card has no clock at all until the cardholder sets one.

The vehicle note pays 536.05 a month, with 144.83 of the first check going to interest and 391.22 to principal. Four years is brief enough that principal drops at a visible pace, which is why the total interest remains under 4,000 dollars.

The card is the opposite case. Paying 200 a month on 8,000 at 22 percent clears the balance in 73 payments and costs 6,551.27 of interest, close to the original balance. At 250 a month it clears in 49 payments. The card issuer recalculates the minimum as the balance drops, so a minimum payment schedule can stretch for decades and cost more than the purchases did.

Two loan designs break the pattern. A balloon loan holds a small check for a set stretch and one large check at the end. An interest-only loan pays no principal for a set stretch, so the balance remains flat and the check jumps when that stretch finishes. Neither builds equity on the chart above. An adjustable rate loan resets on a schedule, so the check and the split change without any action from the homeowner.

The Consumer Financial Protection Bureau explanation of paying down a mortgage walks through the same split, and the FTC guidance on financing a vehicle says that a modest check can hide a longer, more costly loan.

Before you send extra funds

Three steps are useful before a single extra dollar goes out. First, review the agreement for a prepayment penalty. Most US mortgages and auto loans do not charge one, but a few do, and the fee can wipe out the saving.

Second, on a mortgage, find out how the servicer manages extra funds. A payment sent through the normal channel may be held in escrow or applied to the next installment unless it is labeled as principal only. Third, verify on the next bill that the balance moved by the full extra payment.

This calculator assumes a fixed rate, payments on time, no fees added to the balance, and interest charged once a month. An adjustable rate loan changes its payment when the rate resets, so rerun the numbers with the new rate. Property tax, homeowners insurance, mortgage insurance, and HOA dues are distinct from amortization and do not appear in the schedule.

The Consumer Financial Protection Bureau says on its mortgage servicer rules page that even 100 dollars more a month can trim a note by a few years, and it recommends confirming that the funds are applied to principal rather than interest. The schedule in the calculator above shows precisely what that looks like month by month.

A payoff quote when you sell or refinance is distinct from the schedule, and it includes daily interest on the remaining principal. An amortization worksheet in the closing package follows the same rows.