Amortization Schedule Calculator

Background.

On a $300,000 mortgage at 6.5% over 30 years, the first monthly payment of $1,896.20 sends $1,625.00 to interest and only $271.20 to the loan itself. Twelve payments in, you have paid $22,754.40 and the balance has fallen by just $3,353.13. That lopsided start is not a fee or a lender's trick. Interest is charged each month on whatever is still owed, and at the beginning nearly everything is still owed.

An amortization schedule is the month-by-month record of that process. Enter the amount borrowed, the annual interest rate and the term in years, and you get the level monthly payment that clears the loan exactly on time, the total interest that payment implies, and the total of all the payments. Those three figures are the summary line of the schedule; every row underneath follows from one rule, explained below, that you can apply in a spreadsheet to see any month you like.

The shape of the schedule explains things borrowers often discover too late. Equity from repayment builds slowly: on the example loan, ten years of payments retire only $45,670.94 of the $300,000, the principal portion of a payment does not overtake the interest until payment 233, and half the original debt is not repaid until payment 257, more than 21 years in. Selling or refinancing in the early years therefore leaves most of the loan outstanding. The same shape is why an extra $1,000 paid in the first month saves far more than $1,000 paid near the end: it removes principal that would otherwise have been charged interest for decades.

The calculation assumes a fixed-rate, fully amortizing loan repaid monthly, with no fees, no escrow for property tax or insurance, and no change in rate. That describes most fixed-rate mortgages, car loans and personal loans as they are originally scheduled.

What is amortization schedule?

To amortize a loan is to pay it off through equal installments, each of which covers the interest that built up since the last payment and repays a slice of the principal. The schedule is the table of those installments: payment number, the interest part, the principal part and the balance left afterward. Because the balance falls every month, the interest part shrinks and the principal part grows, while their sum stays the same. A loan that reaches exactly zero at the last payment is fully amortizing. Interest-only loans repay no principal for a period, balloon loans leave a large lump to pay at the end, and negatively amortizing loans set payments below the interest due, so their balance rises; none of those follows the schedule computed here.

How to use this calculator.

1. 01Enter as Loan Amount the sum actually borrowed: the price less your down payment, plus any fees you chose to roll into the loan. Leave out property tax, homeowner's insurance and mortgage insurance, which are billed alongside the payment but are not part of the debt.
2. 02Enter the Annual Interest Rate printed on your loan contract or Loan Estimate as the interest rate, not the APR. The APR folds points and fees into a single cost figure, so using it here would slightly overstate the payment. Enter 0 for an interest-free loan; a negative rate is refused.
3. 03Enter the Loan Term in years, from 1 to 50. Fractions work: 5.5 years means 66 monthly payments.
4. 04Partway through a loan? Enter the current balance from your statement, the same rate and the years still to run. The payment that comes back should be close to the one you already pay, and the total interest is what remains to be paid from here.
5. 05Read the monthly payment first, then the total interest. To compare offers, change one input at a time, since a shorter term and a lower rate both cut total interest but affect the monthly payment in opposite directions.

The formula.

The monthly payment is M = P × r ÷ [1 − (1 + r)⁻ⁿ], where P is the loan amount, r the monthly rate (the annual percentage divided by 100 and then by 12) and n the number of payments (years × 12). It is the same as the textbook form M = P × r(1 + r)ⁿ ÷ [(1 + r)ⁿ − 1].

The formula comes from asking which level payment, discounted back to today at the loan's own rate, is worth exactly the amount lent. The bracketed term, divided by r, is the present value of one dollar a month for n months; dividing the loan by it gives the payment. That is also why the loan is cleared precisely at payment n and not before or after.

Each row of the schedule follows the same three steps. Interest for month k is the previous balance × r. The principal repaid is M minus that interest. The new balance is the old one minus the principal. On the example loan the second payment carries $1,623.53 of interest and $272.67 of principal, a shift of about a dollar and a half in a single month that keeps compounding for 30 years.

The totals are built from the payment as you would actually pay it, rounded to the cent: total cost is the rounded payment × n, and total interest is total cost minus the loan amount. Because rounding trims a fraction of a cent each month, a real schedule is left with a few dollars outstanding at the end (about $4.50 on the example loan), which lenders normally add to the final payment.

Monthly compounding is itself a simplification for some loans. Many car loans and personal loans accrue interest daily on the outstanding principal, so a payment that arrives a week late carries more interest and less principal than the schedule shows, and an early one the reverse. Mortgages in the United States are normally scheduled monthly as modeled here.

Rate and term set the result. At 6% the example loan costs $1,798.65 a month and at 7% $1,995.91, so each half point moves the payment by about $100 and the lifetime interest by about $35,000. A zero rate cannot go through that formula, which divides by r, so the calculator switches to the limit: an interest-free loan pays the amount divided by the number of payments, and the total cost is exactly the amount borrowed.

A worked example.

Frequently asked questions.

References& sources.

1. [1]CFPB (2023). "What is an amortization schedule?" Consumer Financial Protection Bureau.
2. [2]Federal Reserve (2023). "Consumer Handbook on Adjustable-Rate Mortgages."
3. [3]Bodie, Z., Kane, A., & Marcus, A.J. (2021). Investments, 12th ed. New York: McGraw-Hill. ISBN 978-1264118393.
4. [4]OCC (2023). "Truth in Lending Act — Regulation Z." 12 CFR Part 1026.
5. [5]CFPB (2015). "TILA-RESPA Integrated Disclosure Rule." 12 CFR Part 1026.
6. [6]HUD (2023). "Amortization Basics." U.S. Department of Housing and Urban Development.