Monthly Payment Mortgage Calculator

One number, and what it is

Most mortgage calculators throw six things at you. This one gives you a single figure: the monthly payment on principal and interest.

That is deliberate, and it is the number people actually come looking for. It is what the lender bills you every month against the loan itself, and on a fixed rate deal it does not move for the entire term. Whether the rate is 6 percent or 9 percent, whether the term is fifteen years or thirty, that one figure tells you whether a loan fits inside your month.

Three inputs, one answer, no scrolling past a wall of results to find it. Below is how it gets there, what the payment is built from, and what else lands on your housing bill that this figure does not cover.

Filling the three boxes

1. Mortgage amount. The sum you are borrowing. Not the price of the house. There is a short section below on this because it is the one mistake worth avoiding.
2. Annual interest rate. Your quoted rate as a percentage, so type 6.5 rather than 0.065.
3. Mortgage term. The number of years you have to repay it.
4. Press Calculate. Reset clears all three and starts you over.

Then change one number and press it again. A mortgage is a set of trade-offs, and the only way to see a trade-off is to move one thing and watch what happens.

Mortgage amount means the loan, not the house

This box wants what you are borrowing. If the house is 400,000 and you are putting 80,000 down, the number that goes in here is 320,000.

Put the full 400,000 in and the payment comes back around 2,528 instead of 2,022, which is roughly 500 a month of imaginary debt. Not a small error to carry around while you are house hunting.

It works this way on purpose. Plenty of people using a payment calculator are not buying a house at all. They are refinancing an existing balance, taking a second loan against a property, or checking what a lender has already quoted them. Every one of those starts with a loan amount and no purchase price. If you would rather start from the price and a deposit, the mortgage calculator does the subtraction for you.

The formula, written the way this tool writes it

This is the standard amortising payment formula. Here is the exact shape the calculator uses:

M = P × r × (1 + r)ⁿ ÷ ((1 + r)ⁿ - 1)

• P is the mortgage amount you typed.
• r is the monthly rate: your annual rate divided by 12, then divided by 100.
• n is the number of payments: term in years multiplied by 12.

You will see the same formula written elsewhere as M = P × r ÷ (1 - (1 + r)^-n), with a negative exponent and no visible numerator. Those two are the same equation. Multiply the second one top and bottom by (1 + r)ⁿ and you land exactly on the first. Different textbooks and different tools just settled on different arrangements of it, so if you compare our working against somebody else's and the shapes look unfamiliar, that is why. The answers agree.

What the formula is looking for, in either form, is the one payment that clears the balance to precisely zero on the final month. Each payment settles that month's interest first, and whatever is left over reduces the principal.

One convention worth naming. Dividing the annual rate by twelve treats your quoted rate as a nominal annual rate carved into twelve equal monthly pieces. That is how US mortgages work, and it matches the Truth in Lending definition of an annual rate as a periodic rate multiplied by the number of periods in a year. Canadian mortgages compound twice a year and will land a little differently.

Doing one by hand

Take a mortgage amount of 320,000, a rate of 6.5 percent, and a term of 30 years.

The monthly rate is 6.5 ÷ 12 ÷ 100 = 0.00541667. The number of payments is 30 × 12 = 360.

Raise 1.00541667 to the power of 360 and you get about 6.9918. That single number is doing most of the work, so it is worth pausing on. It says a sum of money left to compound at this rate for thirty years grows to nearly seven times its size, and your loan is fighting that growth every month.

Now the formula. The top is 320,000 × 0.00541667 × 6.9918 = 12,119.1. The bottom is 6.9918 minus 1 = 5.9918. Divide and you get 2,022.62 a month.

A few more, all at 6.5 percent, so you can see how the shape moves:

Look at the first two rows. Halving the term does not double the payment, it adds about 38 percent. That surprises people, and it is one of the more useful things this calculator will show you in ten seconds.

What the payment is made of in month one

The payment is one number but it does two jobs, and the split between them changes every month.

On that 320,000 at 6.5 percent, the first month's interest is just the balance times the monthly rate: 320,000 × 0.00541667 = 1,733.33. Subtract that from the 2,022.62 payment and only 289.28 is left to reduce what you owe.

So payment number one is about 86 percent interest and 14 percent house.

By the final payment it has completely reversed. The payment is still 2,022.62, but by then only 10.90 of it is interest and 2,011.72 goes at the principal. Same number, opposite job.

This is why the early years feel like nothing is happening. It is also why money paid at the balance early does so much more than the same money paid late, since anything you clear in year two stops accruing interest for the twenty eight years that follow. If you want to see the split for every single month, the mortgage amortization calculator prints the whole schedule.

The rate box and the numbers it takes

Two things to know about what goes in here.

First, it wants your interest rate rather than your APR. The interest rate is the cost of borrowing, and it is what your lender uses to work out the bill. APR is a wider measure that folds in points, broker fees and origination charges, which is why it is usually the higher of the two. Type the APR in here and you get a payment that quietly bills you for your closing costs every month for thirty years. On a US Loan Estimate the interest rate is on page one and the APR is on page three.

Second, the box is scoped to real mortgage rates. It accepts anything from 1 percent up to 50, which covers every ordinary home loan and a fair few unpleasant ones. If you are modelling something below 1 percent, promotional seller financing or a subsidised scheme, the loan payment calculator handles that end of the range.

Small inputs, real consequences. On a 320,000 loan over thirty years, half a percentage point on the rate is about 106 a month and roughly 38,000 across the term.

It works in any currency

The result comes back as a bare number with no currency symbol attached, and that is on purpose.

Nothing in the formula knows or cares whether you are counting in dollars, rupees, pounds or naira. Feed it 320,000 and it returns 2,022.62 in the same units you fed it. So a Nepali borrower checking a bank loan in rupees and an American checking a mortgage in dollars get the same correct answer from the same box.

The one thing to check when you travel is the rate convention rather than the currency. This tool divides the annual rate by twelve, which is right for the US, India, Nepal and most places quoting a monthly-compounded nominal rate. Canada quotes semi annually and will differ slightly.

The rest of your housing bill

The label on the result says principal and interest only, and it means it. In most countries your actual monthly outgoing on a home is larger.

Property tax goes to your local government, usually collected monthly by the lender into escrow. Home insurance is almost always required for as long as the loan exists. Mortgage insurance shows up if your down payment was under 20 percent on a conventional US loan, and it protects the lender rather than you. Association fees apply to condos, co-ops and a lot of newer neighbourhoods.

Principal, interest, taxes and insurance together are what lenders call PITI, and that is the figure that decides affordability. What you get here is the P and the I.

There is a reason to want them separated, though. When you are holding two loan offers, principal and interest is the honest comparison, because one lender may escrow your taxes and insurance while the other leaves you to pay them yourself. Their total payments will look different for reasons that have nothing to do with the loan on offer.

Using it to compare two deals

The fastest way to use a single-answer calculator is to run it twice.

Hold the mortgage amount steady and change only the rate, and you see what a quarter point of negotiation is actually worth to you every month. Hold the rate and change only the term, and you see the real price of paying a loan off faster.

On 250,000 at 6.5 percent, the thirty year payment is 1,580.17 and the fifteen year is 2,177.77. That is 598 more every month for fifteen years, and it buys you 177,000 less interest over the life of the loan. Whether that is a good trade is a question about your cash flow, not about the arithmetic, and no calculator will settle it for you.

One more use worth knowing. If a lender quotes you a monthly payment and you want to check it, run their loan amount, rate and term through here. If their figure is meaningfully above the one you get back, the difference is usually escrow, insurance or fees rolled into the loan, and it is entirely fair to ask which.

Questions people ask

Do I enter the house price or the loan?

The loan. Take the purchase price, subtract your down payment, and enter what is left. On a 400,000 house with 80,000 down, that is 320,000.

What does the payment include?

Principal and interest, and nothing else. Property tax, home insurance, mortgage insurance and association dues are billed separately, often through an escrow account alongside this payment.

Should I use my interest rate or my APR?

The interest rate. APR includes fees and points, so it produces a payment higher than the one you will actually be billed. On a Loan Estimate the interest rate is on page one and the APR is on page three.

Can I use this for a loan in rupees or pounds?

Yes. The result is returned without a currency symbol and comes back in whatever units you entered. Check that your lender quotes a monthly-compounded nominal annual rate, which most do.

Why does halving the term not double the payment?

Because you are also halving the time interest has to accumulate. On 250,000 at 6.5 percent, cutting thirty years to fifteen raises the payment by about 38 percent, not 100 percent, and cuts the total interest by well over half.

Why does my payment show fewer decimals sometimes?

Trailing zeros are dropped in the display, so a payment that works out to exactly 1,500.00 appears as 1500. The value is the same.

Where can I see the month by month breakdown?

The mortgage amortization calculator takes the same three inputs and prints every payment, showing how much of each one goes to interest and how much reduces the balance.

References

The payment formula is the standard actuarial amortisation relation, and the step of dividing the quoted annual rate by twelve follows the Truth in Lending treatment of an annual rate as a periodic rate multiplied by the number of periods in a year. Regulation Z publishes its equations so that they can be used to program calculators, which is exactly what this tool does. The description of what a mortgage payment contains, and the distinction between an interest rate and an APR, follow the Consumer Financial Protection Bureau's consumer guidance.

1. Consumer Financial Protection Bureau (CFPB), Regulation Z, Appendix J to Part 1026: Annual Percentage Rate Computations for Closed-End Credit Transactions. https://www.consumerfinance.gov/rules-policy/regulations/1026/j/
2. Consumer Financial Protection Bureau (CFPB), Regulation Z, § 1026.22 Determination of Annual Percentage Rate. https://www.consumerfinance.gov/rules-policy/regulations/1026/22/
3. Consumer Financial Protection Bureau (CFPB), What Is the Difference Between a Mortgage Interest Rate and an APR? https://www.consumerfinance.gov/ask-cfpb/what-is-the-difference-between-a-mortgage-interest-rate-and-an-apr-en-135/
4. Consumer Financial Protection Bureau (CFPB), What is PITI? https://www.consumerfinance.gov/ask-cfpb/what-is-piti-en-152/
5. Consumer Financial Protection Bureau (CFPB), On a Mortgage, What Is the Difference Between My Principal and Interest Payment and My Total Monthly Payment? https://www.consumerfinance.gov/ask-cfpb/on-a-mortgage-whats-the-difference-between-my-principal-and-interest-payment-and-my-total-monthly-payment-en-1941/