Mortgage Loan Amount Calculator: The Loan a Monthly Payment Repays

This calculator works backwards from a monthly payment: enter the principal-and-interest payment you have in mind, the APR and the term, and see the loan amount that payment would fully repay. It is arithmetic only and says nothing about what a lender would approve.

Formula

P = M × (1 − (1 + r)⁻ⁿ) ÷ r, the present value of n monthly payments of M at monthly rate r = APR ÷ 1200.

Worked Example

$1,800 a month for principal and interest, 6.5% APR, 30 years.

1. r = 6.5 ÷ 1200 = 0.00541667; n = 360
2. (1 + r)⁻³⁶⁰ = 0.143025
3. P = 1,800 × (1 − 0.143025) ÷ 0.00541667 ≈ $284,779.48
4. Total of payments = 1,800 × 360 = $648,000.00; total interest = $363,220.52

Assumptions

• Fixed interest rate for the whole term; payments of equal size at the end of each month.
• Interest compounds monthly at APR ÷ 12.
• No fees, taxes or insurance unless the calculator has a field for them.
• The payment covers principal and interest only. Property tax, insurance, mortgage insurance and HOA dues come on top.

How to read the result

The result is the balance a payment can amortize, not an approval amount. Lenders look at income, debts, credit and the property; ask a lender for a pre-qualification.

Limits and common mistakes

• Do not enter a payment that already includes tax and insurance; subtract them first (the escrow calculator shows them).
• A small change in APR changes the loan amount a lot over 30 years.

Frequently Asked Questions

What loan does $1,800 a month repay at 6.5% over 30 years?

About $284,779, with about $363,221 of interest over the term.

Is this how much I can borrow?

No. It is only the amount the payment repays; a lender decides what it will lend.

What about a 15-year term?

Enter 15 years; the same payment repays a smaller loan but with far less interest.

in m | Monthly payment (principal and interest) | $ | 1800 | 1 | 10000000
in apr | Interest rate (APR) | % | 6.5 | 0.01 | 100
in yrs | Loan term | years | 30 | 1 | 50
out p | Loan amount the payment repays | $ | m * (1 - (1 + apr / 1200) ^ -(yrs * 12)) / (apr / 1200) | 2
out tot | Total of payments | $ | m * yrs * 12 | 2
out int | Total interest | $ | tot - p | 2