Mortgage Calculator
Enter the loan amount, the yearly interest rate and the length of the loan to see the monthly payment.
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Formula
For a fixed-rate loan repaid in equal monthly instalments:
M = P × r × (1 + r)^n ÷ ((1 + r)^n − 1)
Pis the loan amountris the monthly interest rate, the yearly rate divided by 12 and by 100nis the number of monthly payments, the term in years times 12
At 0% interest the payment is P ÷ n. The payment is rounded to cents. Total paid is M × n and total interest is total paid minus P. A real lender's last payment can differ by a few cents.
Worked example
A loan of 300,000 at 6% a year over 30 years:
r = 0.06 ÷ 12 = 0.005andn = 360(1.005)^360 = 6.0226M = 300,000 × 0.005 × 6.0226 ÷ 5.0226 =1,798.65 a month- Total paid is 1,798.65 × 360 = 647,514.00, so the interest is 347,514.00.
Frequently asked questions
How is a monthly mortgage payment calculated?
The payment is the amount that repays the loan and its interest in equal monthly instalments: M = P × r × (1 + r)^n ÷ ((1 + r)^n − 1), where P is the loan amount, r the monthly rate (yearly rate ÷ 12) and n the number of months.
What happens when the interest rate is 0%?
The loan is simply divided into equal parts. A 12,000 loan over one year at 0% costs 1,000 a month.
Does the payment include taxes and insurance?
No. This is the payment for the loan only. Property tax, home insurance and fees are extra and vary by place.
Why is so much of the first payments interest?
Interest is charged on the balance still owed. At the start the balance is highest, so most of each payment is interest. As the balance falls, more of each payment repays the loan.