Mortgage Calculator

What this mortgage calculator gives you

You are probably here because you want to know what a house costs you every month. Fair question. It is the whole question, really.

Give the calculator a home price, a down payment, an interest rate and a term, and it hands back four numbers: the loan amount, the monthly payment, the total you will have paid by the end, and how much of that total was interest.

The monthly payment it returns is your principal and interest. That is the part that goes to clearing the loan, and on a fixed rate deal it is the number that does not move for the entire term. Property tax, home insurance and the rest are collected separately, usually by the lender into an escrow account, and there is a section below on what those add.

So this is the loan half of the answer, worked out exactly. Below is how it gets there, a full example done by hand, and the things worth knowing before you take the number anywhere.

How to use it

1. Home Price. The agreed purchase price of the property, before any fees.
2. Down Payment. The cash you are putting in yourself. Enter it as an amount, not a percentage.
3. Annual Interest Rate. Your quoted interest rate, as a percentage. Not the APR, and there is a whole section below on why that distinction matters.
4. Loan Term. How many years you have to repay. Thirty and fifteen are the usual ones.
5. Press Calculate to see the four results, or Reset to clear the fields and start again.

Change one field at a time and recalculate. That is where the useful information is, because a mortgage is really a set of trade-offs and you can only see a trade-off by moving one thing and watching what happens to the rest.

How the monthly payment is worked out

No secret sauce here. It is the standard amortising loan payment formula, the same one your bank runs, and it looks like this:

M = L × i / (1 - (1 + i)^-n)

Three things feed it:

• L is the loan amount. Home price minus down payment.
• i is the monthly interest rate. The annual rate you typed, divided by 100, then divided by 12.
• n is the number of payments. Term in years, multiplied by 12.

Then two short steps finish it. Total cost is the payment multiplied by the number of payments, and total interest is that total minus the amount you borrowed.

Notice what the formula is hunting for. It wants the one fixed payment that, if you make it every month for n months, leaves the balance at exactly zero on the last day. Not a rupee more, not a dollar less. Every payment clears that month's interest first, and whatever survives goes at the principal.

That "interest first" habit is the entire personality of a mortgage, and we will come back to it.

The dividing of the annual rate by 12 is worth naming, because it is a convention rather than a law of nature. It treats your quoted rate as a nominal annual rate sliced into twelve equal monthly pieces, which is how US mortgages work and how the Truth in Lending rules define an annual rate, as a periodic rate multiplied by the number of periods in a year. Canadian mortgages compound semi annually and will land slightly differently. Worth knowing before you compare across borders.

A worked example: 400,000 house, 20 percent down

Numbers make more sense when you watch them get built, so here is a full run with nothing hidden.

Home price 400,000, down payment 80,000, rate 6.5%, term 30 years.

First the three ingredients:

• L = 400,000 minus 80,000 = 320,000
• i = 6.5 ÷ 100 ÷ 12 = 0.00541667, about 0.5417% a month
• n = 30 × 12 = 360 payments

Now push them through. M = 320,000 × 0.00541667 ÷ (1 - 1.00541667^-360). The top comes out to 1,733.33, the bottom to about 0.857, and dividing one by the other gives 2,022.62 a month.

Then the totals. Total cost is 2,022.62 × 360 = 728,142.36. Take away the 320,000 you borrowed and the interest is 408,142.36.

Type those four inputs into the calculator above and you will get the same four numbers back. That is rather the point of showing the working. If a tool will not show you its arithmetic, you have no way of knowing whether it is doing the arithmetic.

Sit on that interest figure for a second though. You borrowed 320,000 and you will hand back 728,142. The interest alone is more than the loan itself. That is not the bank being greedy, it is simply what thirty years of compounding costs, and it is probably the single most useful thing a mortgage calculator can show you before you sign anything.

Where the first payment actually goes

Here is the part most calculators show you as a table and never explain.

Your first payment is 2,022.62. So where does it go?

The month's interest is settled first, and that is just the balance times the monthly rate. So 320,000 × 0.00541667 = 1,733.33 goes to the lender as interest. What is left, 289.28, is the only part that reduces what you owe.

Which means in month one, about 86 percent of your payment is rent on the money. Roughly 14 percent is buying the house.

Watch what that does over a year. Twelve payments of 2,022.62 is 24,271 of your money gone, and your balance has moved from 320,000 down to about 316,423. You have cleared around 3,577 of principal.

And here is the one that catches people out. Fifteen years in, at the exact halfway point of a thirty year loan, you have not paid off half the house. You have paid off about 27 percent of it, with the balance still sitting near 232,000.

It does flip eventually. Your very last payment is 2,022.62 as well, but by then only 10.90 of it is interest and 2,011.72 is principal. Same payment, completely different job.

This is why money paid at the principal early is worth so much more than the same money paid late. Anything you knock off the balance in year two is removed from every interest calculation for the remaining twenty eight years. The same amount in year twenty eight has almost no time left to work with.

Interest rate or APR? They are not the same number

The rate field wants your interest rate. People very often type their APR in instead, and the two are different animals.

• Interest rate is the cost of borrowing the money, as a yearly percentage. It is what the payment formula runs on, and it is what your lender actually uses to bill you.
• APR is broader. It folds in points, broker fees, origination charges and other costs of getting the loan, which is why your APR is nearly always the higher of the two.

Type the APR in here and the payment that comes back will be too high, because you have quietly asked the formula to charge you your closing fees every month for thirty years. On a US Loan Estimate the interest rate sits on page one under Loan Terms, and the APR sits on page three under Comparisons. Page one is the one you want.

Small thing, real consequence. On our 320,000 example, half a percentage point on the rate moves the payment by about 106 a month and moves the total interest by about 38,286. Worth typing the right number.

None of which means APR is useless. It is the better number for comparing two offers against each other, since it captures the fees one lender is charging and another is not. Use APR to choose the lender, and the interest rate to work out the payment.

What sits on top of principal and interest

Your loan payment is one line on a bill that usually has several. Here is the rest of it.

Property tax. Paid to your local government, and usually collected monthly by the lender into escrow so the bill is covered when it lands. Rates vary enormously by location, so there is no average worth quoting. Look up the real rate for the real county or municipality.

Home insurance. Almost always required by the lender for as long as the loan exists. Also usually escrowed.

Mortgage insurance. If your down payment is under 20 percent on a conventional US loan, expect to pay private mortgage insurance until you have built enough equity. It protects the lender rather than you, which is a detail people find mildly irritating once they learn it. Government backed loans have their own version with their own rules.

Association fees. Condo, co-op, or a neighbourhood with an association. Usually billed separately from the mortgage.

Put together, principal, interest, taxes and insurance are what lenders call PITI. That is the number that decides whether you can afford the house. What this page gives you is the P and the I.

One useful thing falls out of that split. When you are comparing two loan offers, principal and interest is actually the cleaner comparison, because one lender may escrow taxes and insurance while another leaves you to pay them directly, which makes their total payments look different for reasons that have nothing to do with the loan. So compare P and I to judge the loan, then build the full PITI separately to judge the house.

Working out a payment you can actually carry

A payment being calculable is not the same as it being affordable, so it is worth running the number the other way round.

The Consumer Financial Protection Bureau's own budgeting worksheet suggests homeowners aim to keep total debt payments at 36 percent of income or less, and mortgage debt specifically at somewhere in the region of 28 to 35 percent. The helpful detail is that the worksheet defines that mortgage figure as principal and interest only, which is exactly what this calculator returns. So you can use the output directly.

Take our 2,022.62. At 28 percent of gross monthly income, you would be looking at an income of about 7,224 a month, roughly 86,700 a year. Loosen it to 35 percent and the same payment works on about 5,779 a month, or 69,300 a year. Those are guidelines rather than gates, but they tell you quickly whether a house is in your world or somebody else's.

You can also work backwards. Decide the payment you are comfortable with, then find the price that produces it by nudging the home price field until the monthly figure lands where you want. At 6.5 percent over 30 years that gives you roughly:

One caution about a number you will see quoted everywhere. A lot of articles still describe 43 percent debt-to-income as a hard federal ceiling. It was a limit for one specific category of loan, and that limit was replaced with a pricing based test back in 2020. Lenders still use debt-to-income heavily, and 43 is still a common line in practice, but treat it as underwriting habit rather than law.

What a bigger down payment buys you

In this calculator the down payment does one job. It comes off the home price to give the loan amount. Which means every extra unit you put down removes a unit of borrowing, and removes thirty years of interest on that unit along with it.

On our 400,000 house at 6.5 percent over 30 years:

So an extra 40,000 down saves about 253 a month and about 51,000 in interest. Neat and linear, because the formula is linear in the loan amount.

Real life adds one thing the arithmetic cannot show. Crossing the 20 percent line on a US conventional loan is usually what gets you out of mortgage insurance, so the step from 19 to 20 percent tends to save more than the table suggests. Which is why that particular threshold gets talked about so much.

Fifteen years against thirty

Same loan, same rate, different term. Lets run it.

320,000 at 6.5 percent over 30 years is 2,022.62 a month and 408,142.36 of total interest.

The same loan over 15 years is 2,787.54 a month and 181,757.84 of total interest.

So the shorter term costs about 765 more every month and saves about 226,385 across the life of the loan.

That is a genuinely hard trade, and the calculator will not make it for you. More money out the door each month is less money for everything else, including an emergency fund, and being cash poor inside a paid-down house is a real problem that real people have. Shorter terms are also often quoted at slightly lower rates than longer ones, which tilts things a little further, so run your own two rates rather than assuming the rate holds still.

Run both. Then decide with your monthly budget in front of you, not just the total interest figure.

The money you need that is not in the loan

The down payment is the cash requirement everybody plans for. It is not the only one.

On top of it come closing costs, which cover things like the appraisal, title work, lender origination charges, recording fees and prepaid items. They are paid in cash at closing and they are not part of the loan amount, so they do not appear anywhere in the four numbers on this page.

You do not have to guess at yours. Within three business days of applying you get a Loan Estimate, which sets out the projected costs, and at least three business days before you sign you get a Closing Disclosure with the final figures. Comparing those two documents is the single most useful thing you can do with them.

The practical point for budgeting is this: your cash needs to cover the down payment, plus closing costs, plus something left over afterwards. Arriving at closing having spent every last unit on the deposit is a well worn way to start homeownership badly.

How precise these numbers are

The payment is calculated at full precision and rounded to two decimals only when it is displayed, and the totals are worked out from the unrounded payment. Which produces a small thing worth explaining, because people notice it.

The tool shows a payment of 2,022.62 and a total cost of 728,142.36. But 2,022.62 × 360 is 728,143.20, a gap of 0.84. Nothing is wrong. The true payment is 2,022.6176751 and a bit, and you are looking at two correctly rounded numbers taken at different points in the same calculation.

Your lender does something different again. They round each monthly payment to the cent, so the residue accumulates across 360 months and typically gets absorbed into a slightly different final payment. A real amortisation schedule will not match this to the last cent either, and that is expected.

The model behind the numbers is the standard fixed rate deal: one rate for the whole term, twelve equal payments a year made at the end of each month, no fees rolled into the balance, and nothing paid ahead of schedule. If your loan has an adjustable rate, a stub period between closing and your first payment, points financed into the balance, or you plan to overpay, your figures will drift from these, and the loan payoff and mortgage overpayment tools are better suited to those questions.

Treat the payment as accurate and the totals as accurate to within about a unit of currency. For contract-grade figures, take them from the lender's own schedule. This is a planning and comparison tool, not a quote, and not financial advice.

Questions people ask

Is this my full monthly mortgage payment?

It is the principal and interest portion. Add property tax, home insurance, mortgage insurance if it applies, and any association fees to reach your real monthly outgoing. Those are frequently collected by the lender into an escrow account alongside the loan payment.

Should I enter my interest rate or my APR?

The interest rate. APR includes points and fees, so entering it inflates the payment. On a US Loan Estimate the interest rate is on page one and the APR is on page three.

Why is so much of my early payment going to interest?

Because interest is charged on the outstanding balance, and early on the balance is nearly the whole loan. On the example above the first payment is 86 percent interest. That proportion shifts every single month until the final payment is almost entirely principal.

Halfway through a 30 year loan, do I own half the house?

No, and this surprises almost everyone. Fifteen years into the example above you have repaid about 27 percent of the principal. The balance only falls quickly in the closing years.

Does this work for a loan outside the US?

The maths works for any fixed rate amortising loan in any currency. The convention is the thing to check. This tool divides the annual rate by twelve, which suits US and Indian style monthly compounding but not Canadian semi annual compounding.

Why does total cost not equal the payment times the number of months?

Rounding. The totals come from the full precision payment and are rounded once, at display. The gap is under a unit of currency on a typical loan.

Does a bigger down payment always save money?

On interest, yes, and in a straight line. Whether it is the best use of that cash is a different question, since money locked inside a house is money you cannot reach in an emergency. The one real cliff is the 20 percent mark on US conventional loans, where mortgage insurance usually falls away.

Is a shorter term always better?

It always costs less in total interest and always costs more every month. On the example above that is 226,385 saved in exchange for 765 more per month for fifteen years. Which of those matters more depends on your cash flow, not on the arithmetic.

What income do I need for a given payment?

As a rough sighting shot, divide the principal and interest payment by 0.28 to get the monthly gross income that fits the more conservative guideline, or by 0.35 for the looser one. On a 2,022.62 payment that is roughly 7,224 or 5,779 a month.

References

A note on where the figures and definitions come from. The payment formula is the standard actuarial amortisation relation, and the step of dividing the annual rate by twelve follows the Truth in Lending definition of an annual rate as a periodic rate multiplied by the number of periods in a year, set out in Regulation Z. The regulation publishes its equations specifically so they can be used to program calculators. Everything on what a monthly payment contains, on interest rate against APR, and on the affordability guidelines follows the Consumer Financial Protection Bureau's own material.

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 PITI? https://www.consumerfinance.gov/ask-cfpb/what-is-piti-en-152/
4. 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/
5. 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/
6. Consumer Financial Protection Bureau (CFPB), Your Money, Your Goals: Debt-to-Income Calculator, toolkit worksheet. https://files.consumerfinance.gov/f/documents/cfpb_your-money-your-goals_debt_income_calc_tool_2018-11_ADA.pdf
7. Consumer Financial Protection Bureau (CFPB), Qualified Mortgage Definition Under the Truth in Lending Act (Regulation Z): General QM Loan Definition, final rule, December 2020. https://www.consumerfinance.gov/rules-policy/final-rules/qualified-mortgage-definition-under-truth-lending-act-regulation-z-general-qm-loan-definition/