Amortization Calculator

Interest in month k = balance × r, principal in month k = A − interest, and the new balance = old balance − principal

P

The amount borrowed — the original loan balance

r

Monthly interest rate: the annual rate divided by twelve

A

The level monthly payment, rounded to the cent

k

The month being looked at, counting from one

B

The loan balance still outstanding after that month's payment

Use it whenever the payment is not the whole story. If you are deciding between two loans with the same payment but different terms, the amortization schedule is what separates them: the shorter one pays the balance down visibly from the start, the longer one spends years on interest before the balance moves. If you are considering overpaying, the first-month figures here tell you how much of the loan is still exposed to interest — the reason a lump sum early in the term saves far more than the same money later. And if you want to know what you would still owe if you sold or refinanced in five years, the balance column of the schedule is the figure a settlement statement would show, minus the day-to-day interest between the last payment and the payoff date.

1. 250,000 at 6% over thirty years

   1. Monthly rate: 6 ÷ 12 = 0.5% a month, which is 0.005 as a decimal
   2. Payment: 250,000 × 0.005 × 1.005^360 ÷ (1.005^360 − 1) = 1,498.88
   3. First month's interest: 250,000 × 0.005 = 1,250.00 — that is the whole balance for one month
   4. First month's principal: 1,498.88 − 1,250.00 = 248.88
   5. Share of the first payment going to principal: 248.88 ÷ 1,498.88 = 16.6%
   6. Total interest: 539,593.37 paid − 250,000 borrowed = 289,593.37

   This is the page's default and the loan behind the reference table below. Sixteen point six percent is the number to remember: in the first month, five sixths of what you pay is rent on the money, and only a sixth reduces the loan.

2. The same 250,000 at 6%, but over fifteen years

   1. The first month's interest is unchanged: 250,000 × 0.005 = 1,250.00, because the opening balance is the same
   2. Payment over 180 months: 2,109.64, which is 610.76 more a month than the thirty year payment
   3. First month's principal: 2,109.64 − 1,250.00 = 859.64
   4. Share going to principal: 859.64 ÷ 2,109.64 = 40.7%
   5. Total interest: 379,735.85 − 250,000 = 129,735.85 — 159,857.52 less than the thirty year loan

   Same loan, same rate, half the term: the first payment's principal more than triples from 248.88 to 859.64, and the loan is paid off before the interest can compound into six figures. The extra 610.76 a month buys a saving of 159,857.52.

3. 250,000 at 0% over thirty years

   1. Zero rate: nothing accrues, so the first month's interest is 0.00
   2. Payment: 250,000 ÷ 360 = 694.44, which is simply the loan divided by the number of months
   3. First month's principal: 694.44 − 0.00 = 694.44 — the entire payment
   4. Share going to principal: 100%
   5. Total interest: 0.00 over the term, so 250,000 is the whole of what is repaid

   The limiting case, and the one that makes the point clearest: with no interest there is nothing to amortize against, every payment reduces the balance, and the split is 100% principal from the first month to the last.

The page cannot print your own schedule, and that is a structural limit rather than an omission: a month-by-month amortization schedule has one row per month, up to six hundred of them, and this page is built before your inputs exist — the tables here are produced when the site is built, so they can only describe a fixed example loan. The example is 250,000 at 6% over thirty years, and the balance column of that table is the one to read if you want to see how slowly a long loan pays down. What the calculator itself gives you is the first month's split plus the totals for your own numbers; to see your own schedule, the same figures appear on any lender's statement or annual summary. Two smaller caveats. Each month's interest is rounded to the cent before it is added up, which is what a lender does, so a schedule built from unrounded figures will differ from this by a few cents at the end. And the schedule assumes the rate stays where you put it and that no extra payments are made — a single overpayment early on reorders everything after it.

What is an amortization schedule?

A table of every payment on a loan, one row per month, showing how much of that payment is interest, how much is principal and what the loan balance is afterwards. The payment stays the same from row to row while the split inside it changes: interest is charged on the balance, the balance falls, so interest falls and principal rises. The same table is what a lender sends you as an annual statement.

Why is almost all of my first payment interest?

Because interest is charged on the whole balance and the balance is at its largest at the start. On 250,000 at 6%, one month's interest is 250,000 × 0.005 = 1,250.00. If the payment is 1,498.88, only 248.88 is left to reduce the loan. Nothing is wrong: the loan is simply most expensive to hold in the first month, and cheapest in the last.

How much of my loan is left after fifteen years of a thirty year mortgage?

More than you would guess. On 250,000 at 6% over thirty years the balance at the end of year fifteen is 177,621.13 — a little over seventy percent of the loan, after half the payments have been made. The balance only starts falling quickly in the last third of the term, which is why overpaying early is worth so much more than overpaying late.

Does the principal and interest in the schedule add up to the loan?

Yes, and it is a useful check. Every payment is split into interest and principal with nothing lost, so the principal column of a complete schedule adds up to the amount borrowed and the interest column adds up to the total interest — on the 250,000 example, 289,593.37. If your own figures are a few cents out, it is the rounding of each month's interest to the cent, not an error.

Can I see the amortization schedule for my own loan here?

Not month by month: the table on this page is generated when the site is built, from a fixed example loan, and a schedule with one row per month would need up to six hundred rows. What the calculator returns for your own numbers is the first month's split and the totals, and any lender will give you the full schedule for your loan on request.

What is the difference between amortization and a repayment schedule?

They describe the same table from two directions. Amortization is the process — the balance being paid down by degrees as each payment's principal share grows. A repayment schedule is the document that records it. Where the payment is fixed, the schedule is fully determined by the amount, the rate and the term; where you choose the payment instead, it is determined by how much you pay, which is why the answer comes back as a number of months.

• Compound Interest Calculator — why interest charged on a balance every period makes the early payments interest-heavy — U.S. Securities and Exchange Commission (Investor.gov)
• Mortgage Debt Outstanding — the balance-versus-payment picture across the United States mortgage market — Board of Governors of the Federal Reserve System (United States)