Mortgage Calculator

The amortization formula behind the monthly figure

The payment is the standard fixed-rate amortizing loan formula: M = P × i × (1 + i)^n ÷ ((1 + i)^n − 1), where P is the loan amount, i is the monthly rate (annual rate ÷ 100 ÷ 12) and n is the number of monthly payments (years × 12). If the rate is 0, the tool simply divides the loan amount by the number of payments.

With the default inputs, P is 350,000 − 70,000 = 280,000, i is 6.5 ÷ 100 ÷ 12 = 0.0054167 and n is 360. The growth factor (1 + i)^360 comes to 6.9918, so M = 280,000 × 0.0054167 × 6.9918 ÷ 5.9918 = 1,769.79.

Total paid is the unrounded monthly payment multiplied by 360, which gives 637,124.57, and Total interest is that figure minus the 280,000 borrowed: 357,124.57. Because the multiplication uses the unrounded payment, the total can differ by a few cents from 1,769.79 × 360.

How rate and term move the numbers

Two percentage points of interest change the monthly payment on this loan by 368 and the lifetime interest by more than 132,000. Shortening the term from 30 to 15 years raises the payment by 669 a month but cuts total interest by almost 200,000, which is the trade-off most borrowers weigh.

Using the down payment field for what-if checks

The down payment is simply subtracted from the price, so it doubles as a way to test any reduction in the amount borrowed. Raising it from 70,000 to 105,000 on the default home drops the loan to 245,000, the monthly payment to 1,548.57 and total interest to 312,484.00.

Lenders express the down payment as a share of the price: 70,000 on 350,000 is 20%, the level at which US lenders typically stop requiring private mortgage insurance. Divide your down payment by the price to see where you stand.

What the estimate deliberately leaves out

• Property tax, homeowners insurance, HOA dues and mortgage insurance are not included, so an escrowed monthly bill from a lender will be higher than the figure here.
• Closing costs, origination fees and discount points are ignored; they change the effective cost of the loan but not the scheduled payment.
• The rate is assumed fixed for the whole term and the payment constant. Adjustable-rate loans and overpayments need a different calculation.
• The rate is treated as a nominal annual rate compounded monthly, which is the US convention. Lenders in some countries, Canada for example, quote rates compounded semi-annually, so their payment can differ by a few dollars.
• Nothing is shown if the down payment equals or exceeds the price, or if the term is zero, because there is then no loan to amortize.

Reading the results before you talk to a lender

A common affordability rule keeps housing costs at or below 28% of gross monthly income. Add your estimated tax and insurance to the Monthly payment shown here and compare the sum with 28% of your income to see whether the loan fits that guideline.

Total interest is the number to watch when choosing between offers. A slightly higher rate with lower fees can still cost more over 30 years, and the table above shows how steeply interest climbs with each half point.