How to use the calculator
- Enter the amount you will borrow — the price minus your down payment — the annual interest rate and the term in years. The results update as you type.
- Read the two result cards. Fixed payment is the standard mortgage in the US, UK and most of the world: the same payment every month. Equal principal repays the same share of the loan each month, so payments start higher and fall; it is common in China and some European countries.
- Open Extra payments to add one or more lump sums. Choose whether to keep your payment and finish sooner, or keep the end date and lower the payment.
- Scroll through the amortization schedule by year, or tick Show every month. Download it as CSV to open in a spreadsheet.
The formula behind the payment
With a fixed-payment (annuity) loan, the monthly payment M on a principal P, at a monthly rate r = annual rate ÷ 12, over n months is:
M = P × r / (1 − (1 + r)^−n)Each month the lender charges interest on the balance that is still owed — balance × r — and the rest of the payment reduces the balance. Early on the balance is large, so most of the payment is interest; by the end almost all of it is principal. That is why the first years of a 30-year mortgage barely dent the loan, and why extra payments made early save the most.
With equal principal, the principal part is simply P ÷ n every month and interest is added on top, so the payment falls by a fixed amount (P ÷ n × r) each month. Total interest is lower because the balance shrinks faster, and its exact value is r × P × (n + 1) ÷ 2.
Rounding to the cent
Payments are made in whole cents, so this calculator rounds the payment and each month's interest to the cent, as lenders do. Those small differences accumulate, so the final payment is adjusted to bring the balance exactly to zero instead of leaving a few cents behind or overshooting. The same rounding explains why the equal-principal total below differs from the textbook formula by about a dollar.
Rate, APR and what is left out
Enter the note rate — the interest rate on the loan itself. The APR shown on a US Loan Estimate is higher because it spreads fees and points over the life of the loan; it is useful for comparing offers but is not the rate the payment is calculated from. The payment here covers principal and interest only. A lender's monthly figure usually also includes property tax and homeowners insurance held in escrow, and private mortgage insurance (PMI) if you put down less than 20 percent on a conventional loan.
Worked examples
A $300,000 loan at 6% for 30 years. The monthly rate is 0.5% and there are 360 payments. The formula gives a payment of $1,798.65. Over the whole term you pay $347,515.44 in interest, more than the amount borrowed. Because of cent rounding, the 360th payment is $1,800.09 rather than $1,798.65.
The same loan with equal principal. The principal part is $833.33 a month. The first payment adds $1,500.00 of interest, for $2,333.33; the second is $2,329.16, and the last is $838.70. Total interest is $270,751.07 — about $76,764 less than the fixed payment. The formula r × P × (n + 1) ÷ 2 gives exactly $270,750; the extra $1.07 comes from rounding each month to the cent.
One extra payment of $50,000 in month 12.
| Choice after the extra payment | Months to pay off | Total interest |
|---|---|---|
| no extra payment | 360 | $347,515.44 |
| keep the payment, finish sooner | 244 | $187,861.54 |
| keep the term, lower the payment to $1,495.15 | 360 | $291,895.51 |
Finishing sooner saves far more interest — about $104,000 more than lowering the payment — because the balance stays smaller for longer. Lowering the payment is the safer choice if your income is uncertain.
A zero-interest loan of $100,000 over 10 years is simply 100,000 ÷ 120 = $833.33 a month, with a final payment of $833.73 to cover the 40 cents lost to rounding.
Limits
- Fixed rate only. Adjustable-rate mortgages change their rate after the initial period, and the schedule would change with it. You can approximate an ARM by running the calculator again with the expected new rate for the remaining balance.
- Principal and interest only. Taxes, insurance, PMI, HOA dues and closing costs are not included.
- Monthly payments. Biweekly schedules, interest-only periods and balloon payments are not modelled.
- Lender conventions differ slightly. Some lenders compute interest on a daily basis or round differently, which can shift individual payments by a few cents. Your loan documents are authoritative.
- Not financial advice. Whether to prepay a mortgage or invest the money depends on rates, taxes and your circumstances; see the guide on that question for how to compare the two.
Frequently asked questions
How is the monthly mortgage payment calculated?
With the annuity formula M = P × r / (1 − (1 + r)^−n), where P is the loan amount, r the monthly interest rate and n the number of months. For $300,000 at 6% over 30 years that is $1,798.65.
Does the payment include taxes and insurance?
No. It is principal and interest only. Lenders usually add property tax, homeowners insurance and, where required, PMI to the monthly amount they collect.
Is it better to shorten the term or lower the payment after an extra payment?
Shortening the term saves more interest because the balance falls faster. Lowering the payment gives you more room in your monthly budget. The example above shows the difference for a $50,000 prepayment.
What is the difference between fixed payment and equal principal?
A fixed payment is the same every month. Equal principal repays the same portion of the loan each month, so payments start higher and fall over time, and total interest is lower.
Is anything I enter saved or sent anywhere?
No. The calculation runs in your browser, and the numbers you enter are not stored or transmitted.