Formula
Fixed-rate mortgage, the annuity formula used by the CFPB and by every amortization schedule. Tax, insurance, and HOA are added after the formula. They are not financed.
M = P × r(1 + r)^n / ((1 + r)^n − 1)
r = annual rate ÷ 12
n = years × 12
a zero rate is P ÷ n
Each month, interest is the balance times r. The rest of M reduces principal. Extra principal is applied after that. The test for this page is a $200,000 loan at 6% for 30 years: the payment is $1,199.10, 360 months retire it, and the interest is payment × 360 minus the principal, within two cents.
Worked examples
$240,000 price, $40,000 down, 6%, 30 years. Loan $200,000. Principal and interest $1,199.10. With $2,400 of tax and $1,200 of insurance the housing payment is $1,499.10.
The same loan with $200 extra each month. The balance reaches zero before month 360, and the interest falls by more than the extra payments cost.
Reference
Principal and interest only, 30 years, no extra payment. Tax and insurance are not in this column.
| Loan | Rate | Monthly P&I |
|---|---|---|
| $200,000.00 | 6% | $1,199.10 |
| $320,000.00 | 6.5% | $2,022.62 |
| $400,000.00 | 7% | $2,661.21 |
| $500,000.00 | 5.5% | $2,838.95 |
Questions
How is a mortgage payment calculated?
The fixed-rate payment is principal times the monthly rate times (1 + rate) to the number of months, divided by that same power minus one. On a $200,000 loan at 6% for 30 years the principal and interest is $1,199.10. A zero rate is just the principal divided by the number of months.
What is included in the monthly number?
Principal and interest come from the formula. Property tax, insurance, and HOA are added on top and do not change the interest. Extra principal shortens the loan. It is applied after the scheduled principal, and it cannot pay the balance below zero.
Does this include PMI?
No. Private mortgage insurance depends on the lender and the loan-to-value. This page keeps the annuity, the tax, the insurance you type, and the HOA. Add PMI to the insurance line if you want it in the monthly total.
Why does the old calculator.pro mortgage URL land here?
The previous site had a mortgage calculator that other sites linked to. This is a fixed-rate schedule in the same place, so those links still open a mortgage calculator.
Sources
- Fixed-rate annuity: M = P r (1+r)^n / ((1+r)^n − 1). Consumer Financial Protection Bureau mortgage formula. A zero rate is principal divided by the number of months.