Mortgage calculator

How is a mortgage payment calculated?

A repayment mortgage has a fixed monthly payment set so that, after the last payment, the loan and all its interest are paid off. The formula is M = L x i x (1 + i)^n / ((1 + i)^n - 1), where L is the loan, i the monthly interest rate (the annual rate divided by 12) and n the number of monthly payments.

With the defaults above, a $400,000 home with a 20% down payment leaves a $320,000 loan. At 6.5% over 30 years, i = 0.065 / 12 and n = 360, so the payment is $2,022.62 a month. Over 30 years you pay $728,142 in total, of which $408,142 is interest. Each month, interest is charged on the balance still owed and the rest of the payment reduces the loan. In the first year that means $20,695 of interest and only $3,577 off the loan.

How do you calculate a mortgage payment by hand?

Work it in four steps, keeping plenty of decimal places until the end. Using the $320,000 loan at 6.5% for 30 years:

1. Monthly rate: i = 0.065 / 12 = 0.00541667, keeping the full value in your calculator.
2. Growth factor: (1 + i)^360 = 6.991798.
3. Top line: L x i x (1 + i)^n = 320,000 x 0.0054167 x 6.991798 = 12,119.12.
4. Divide: 12,119.12 / (6.991798 - 1) = 12,119.12 / 5.991798 = $2,022.62.

Rounding too early moves the answer: using 0.0054 as the monthly rate gives $2,018.41, more than $4 out. The calculator carries full precision and shows the result to the cent. Open Show the working under the result to see these steps with your own numbers. At a 0% rate the formula does not apply, and the payment is simply the loan divided by the number of months.

Worked examples in three currencies

Every currency uses the same arithmetic, and no amount is converted between currencies. These examples use rates chosen for illustration, not quotes from any lender.

The 15-year loan costs $764.92 more a month than the 30-year one but saves $226,385 of interest. In the dirham example, interest over 25 years comes to about two thirds of the amount borrowed. Choose a currency in the selector and the symbols and decimals follow it; untouched defaults are resized to round amounts for that currency.

How do the rate, the term and the down payment change the payment?

On the $320,000, 30-year loan, each percentage point on the rate adds between about $206 and $223 to the monthly payment, and the effect on total interest is far larger:

A longer term lowers the payment but raises the interest. At 6.5%, the same loan costs $2,787.54 a month over 15 years, $2,385.83 over 20, $2,160.66 over 25 and $2,022.62 over 30, while total interest climbs from $181,758 to $408,142. A bigger down payment shrinks the loan itself: on the $400,000 home, putting down 10% instead of 20% raises the loan to $360,000 and the payment to $2,275.44, and 30% down cuts it to $1,769.79.

How does an amortization schedule work?

An amortization schedule lists every payment and how it splits between interest and principal. Because interest is charged on the balance, early payments are mostly interest and later ones mostly principal. On the default loan, the principal part of the payment first exceeds the interest part in month 233, in year 20. After 5 years the balance is still $299,555, and after 10 years $271,284, even though $242,714 has been paid by then.

The schedule under the calculator shows one row per year: what you paid, the interest, the principal and the balance at year end. Choose Each month under the extra options to see every payment. The chart of where each year's payments go shows the same shift as two shaded bands, and the balance chart beside the result shows how slowly the debt falls at first.

How much can mortgage overpayments save?

Any extra money paid off the loan stops being charged interest for the rest of the term, so early overpayments save the most. The calculator keeps the normal payment the same and lets the loan finish sooner:

• $200 extra every month on the default loan clears it in 23 years 5 months, 6 years 7 months early, and saves $105,429 of interest.
• A single $10,000 lump sum at the end of year 1 ends the loan 2 years 5 months early and saves $50,537.
• £100 extra a month on the £250,000, 4.5%, 25-year loan ends it 2 years 10 months early and saves £21,871.

Paying half the monthly payment every two weeks, often called an accelerated biweekly schedule, adds up to 13 monthly payments a year instead of 12. You can approximate it here with an extra monthly payment of one twelfth of the normal payment: $168.55 on the default loan, which ends it 5 years 10 months early and saves $93,073. These figures are an approximation, because a real biweekly plan pays every two weeks rather than once a month. A loan can limit or charge for overpayments, so check its terms before paying extra.

Interest-only or repayment: what is the difference?

On an interest-only mortgage the monthly payment covers the interest and nothing else, so the balance never falls. On the $320,000 loan at 6.5% that payment is $1,733.33, which is $289.28 a month less than the repayment payment of $2,022.62. Over 30 years the interest-only borrower pays $624,000 of interest and still owes the full $320,000 at the end, a total of $944,000. The repayment borrower pays $408,142 of interest and owes nothing.

Choose the Interest-only tab to see your own figures beside the repayment payment for the same loan. The balance chart shows the two loans side by side: a flat line for interest-only, a falling curve for repayment. The final balance has to come from savings, the sale of the home or a new loan, and the calculator does not model any of those.

How do you calculate a mortgage payment in Excel?

Excel's PMT function returns the payment for a loan with a fixed rate and equal payments. Its syntax is PMT(rate, nper, pv, [fv], [type]): rate is the interest rate per period, nper the total number of payments and pv the loan amount. Microsoft's documentation says to keep the units consistent, so for monthly payments divide the annual rate by 12 and multiply the years by 12.

For the default loan, =PMT(6.5%/12, 30*12, -320000) returns 2,022.62, the same as the calculator. Microsoft's own examples enter the loan as a positive amount and show the payment in brackets, as a negative number. This formula enters the loan as -320000, so the payment comes out positive. Leave type out, or set it to 0, for payments at the end of each month, as this calculator assumes.

Common mistakes and what this calculator leaves out

• Using the annual rate as the monthly rate. 6.5% a year is 0.5417% a month.
• Comparing payments, not total cost. A longer term or an interest-only loan lowers the payment and raises what you pay overall.
• Ignoring the costs around the loan. Property tax, insurance and fees can add a large amount each month; enter them under the extra options to see a total.
• Treating a rate as fixed for the whole term. Variable and introductory rates change, and the payment changes with them.

The calculator assumes one fixed rate for the whole term, monthly payments at the end of each month and interest charged monthly at the annual rate divided by 12. Some loans compound or quote rates differently, so check your loan agreement. It does not include arrangement or closing fees, mortgage insurance, rate changes, or purchase taxes such as UK Stamp Duty Land Tax, which are set by each country's own rules and can be large. It also does not assess what a lender would let you borrow.

Glossary

Principal: the amount borrowed, and later the part of each payment that reduces it. Down payment (deposit): the share of the price paid upfront. Term: the number of years over which the loan is repaid. Amortization: paying a loan off in regular installments of interest and principal. Repayment mortgage: each payment covers interest and part of the loan, so the balance reaches zero at the end. Interest-only mortgage: payments cover interest only and the whole loan is due at the end. Overpayment: money paid on top of the required payment to reduce the balance faster. Balance: what is still owed after a payment.

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