How to build an amortization schedule
Take the loan in the answer above: $300,000 borrowed at 7.40% a year and repaid in 360 monthly payments.
- Divide the annual rate by twelve to get the rate for one month. It does not come out exactly, so the figure below is rounded; the calculator keeps the exact twelfth. 7.40% ÷ 12 ≈ 0.6167% a month
- Put it into the standard loan payment formula, where P is the amount borrowed, r the monthly rate and n the number of monthly payments. P × r ÷ (1 − (1 + r)^−n) = $300,000 × 0.6167% ÷ (1 − (1 + 0.6167%)^−360) = $2,077.14
- This calculator rounds each month's interest to two decimal places and uses the smallest payment that brings the balance to exactly zero after 360 payments. Here that is the same figure: $2,077.14 a month.
- In the first month the interest is the balance times the annual rate, divided by twelve and rounded to two decimal places, and the rest of the payment repays the loan. $300,000 × 7.40% ÷ 12 = $1,850 interest $2,077.14 − $1,850 = $227.14 repaid $299,772.86 still owed
- Every month repeats that on a smaller balance, and the last payment, $2,076.56, only clears what is left. Over 360 payments you pay $747,769.82 in all, and everything above the amount borrowed is interest. $747,769.82 − $300,000 = $447,769.82 interest
- Payment 360 is the last row, and it only has to clear what is left: the balance after the row before it, plus that month's interest worked out the same way. $2,063.83 × 7.40% ÷ 12 = $12.73 interest $2,063.83 + $12.73 = $2,076.56, the last payment
Every row of the schedule above is built the same way, and that is where the $2,077.14 payment and the $447,769.82 of interest in the answer come from.
What an amortization schedule actually shows
Amortization is the process of paying a debt down to nothing with a series of equal payments. The schedule is the row-by-row record of that process: for each month, what the payment was, how much of it the lender kept as interest, how much came off the balance, and what was left afterwards.
The mechanism is simple enough to state in a sentence. Interest is charged on what you still owe, your payment covers that interest first, and whatever is left reduces the balance. Because the balance is smaller next month, so is the interest, so a slightly larger slice of the same payment goes on the balance. Repeat three hundred and sixty times and you have a mortgage.
What the table makes visible is how lopsided the early years are. The first payment on a long loan is mostly interest; the last is almost entirely balance. Nothing about that is a trick or a penalty. It falls straight out of charging interest on an amount that starts large.
The three moments worth looking for
A three-hundred-row table hides its own answer. The summary above the schedule names the three moments people are actually looking for.
The crossover is the first month where more of your payment reduces the balance than is taken as interest. On a thirty-year loan at an ordinary rate it lands somewhere around year nineteen, which surprises most people the first time they see it.
The halfway point is the first month the balance is under half of what you borrowed. It is not the middle of the term, and on a long loan it is nowhere near it.
The last payment is almost always a few cents smaller than the rest, and the schedule shows exactly what it is.
Paying extra, and why timing dominates
An extra amount added to every instalment goes entirely against the balance, because the interest for that month has already been covered. Removing balance early removes every future month of interest that balance would have generated, which is why an overpayment in year one is worth many times the same amount in year twenty-five.
Put a figure in the extra payment field and the schedule below switches to the shorter loan that results, so the table you read is the one you would actually pay. The summary keeps both: what the contractual loan would have cost, and what the accelerated one costs instead.
Common questions
Why does my lender's schedule differ by a cent or two?
Because interest is rounded to the cent every month and the textbook formula assumes it is not. Any two honest implementations land within a cent of each other, and which side they fall on depends on the rounding convention applied. A difference bigger than that means something other than rounding differs: a fee rolled into the balance, a different day-count convention, or a payment date that is not a whole month after the last one.
Why is every row's payment identical except the last?
The level payment is set to the smallest amount that clears the loan within the term. Because it is a whole number of cents it can never divide the balance exactly, so a small remainder survives to the end and the final instalment collects only that. This is what most lenders do. A schedule where every single payment is identical has hidden a few cents somewhere.
Can I see the schedule by year instead?
Yes, with the view control beside the extra payment field. The yearly view folds twelve rows into one and is easier to take in; the monthly view is the one to use when you are checking a specific payment against a statement.
What is the difference between this and the loan calculator?
The loan calculator answers what the payment is, with a chart and a yearly summary. This page answers where each payment goes, month by month. They share the same arithmetic and differ in what they put in front of you.
Does this work for anything other than a mortgage?
Yes. Car loans, personal loans and student loans on a fixed rate with level monthly payments all amortize the same way, and the schedule is built identically. What it does not cover is anything with a variable rate, an interest-only period, a balloon payment at the end, or a balance that can grow again, such as a credit card.
Is anything I type stored?
No. The calculation runs on our server from the values in the address bar, nothing is written down, and the access log for this site drops the query string precisely so that the numbers you enter are never recorded.
Sources
No figure on this page is read from a table, so there is nothing to source. What these documents define is the regulated rate this calculator deliberately does not compute:
How the payment is worked out
The instalment is the smallest monthly payment that brings the balance to exactly zero within the term. Interest for a month is the balance times the yearly rate divided by twelve, rounded to the cent in a single step, so the twelfth is never rounded on its own. Every row adds up and the final payment is whatever is left, which is normally a little smaller than the rest.
It prices a loan from the nominal rate alone, so it is not an APR or an APRC.