How to use
- Enter the payment you can put toward principal and interest. If the number you have in mind already includes tax or insurance, the principal will be overstated.
- Enter the APR and the term in years.
- Press Calculate. The hero is the principal.
- The other lines are the total of every payment and the interest inside that total.
How it's calculated
With r = APR ÷ 12 and n = years × 12 rounded, principal = payment × ((1+r)^n − 1) ÷ (r × (1+r)^n). At a zero rate, principal = payment × n.
Total paid = payment × n. Interest = total paid − principal.
Worked example
A $1,500 payment at 6 percent for 30 years supports about $250,187.42 of principal. The payments add up to $540,000, so the interest is about $289,812.58. If $400 of that $1,500 is tax and insurance, only $1,100 belongs in this box.
Assumptions
A fixed payment, a fixed APR, and a fully amortizing loan. No down payment is subtracted because the result is already the principal, not a purchase price.
FAQ
Is the result a home price?
No. It is the amount borrowed. A purchase price would add a down payment and subtract costs that are not in this form.
Where do taxes and insurance go?
Leave them out of the payment, or subtract them before you type. This formula treats the whole payment as principal and interest.
How is this different from the mortgage calculator?
The mortgage calculator starts from principal and finds the payment. This page starts from the payment and finds the principal.
Does a shorter term raise the principal?
No. The same payment over fewer months supports a smaller principal and usually less interest.