Loan & Mortgage Calculator

Work out monthly payments and see a full amortization schedule for any loan or mortgage.

The formula

The level periodic payment that fully repays a loan or mortgage of principal \(P\). \(i = r/n\) is the periodic rate and \(N = nt\) the total number of payments.

$$PMT = \dfrac{P \times i}{1 - (1 + i)^{-N}} \quad\text{or}\quad PMT = \dfrac{P \times \frac{r}{n}}{1 - \left(1 + \frac{r}{n}\right)^{-nt}}$$

The loan amount that corresponds to a known periodic payment \(PMT\), where \(i = r/n\) is the periodic rate and \(N = nt\) the total number of payments.

$$P = PMT \times \dfrac{1 - (1 + i)^{-N}}{i} \quad\text{or}\quad P = PMT \times \dfrac{1 - \left(1 + \frac{r}{n}\right)^{-nt}}{\frac{r}{n}}$$

The outstanding balance after \(k\) payments have been made, with \(N - k\) payments still remaining. \(i = r/n\) is the periodic rate and \(N = nt\) the total number of payments.

$$B_{k} = PMT \times \dfrac{1 - (1 + i)^{-(N - k)}}{i} \quad\text{or}\quad B_{k} = PMT \times \dfrac{1 - \left(1 + \frac{r}{n}\right)^{-(nt - k)}}{\frac{r}{n}}$$

How to use this calculator

  1. Enter the loan amount (the amount you're borrowing).
  2. Set the annual interest rate as a percentage.
  3. Choose the payment frequency (monthly for most mortgages).
  4. Enter the loan term in years.
  5. Read your payment, total interest, and a year-by-year amortization schedule below.

How it works

A loan or mortgage is repaid in equal payments that cover both interest and principal. Early on, most of each payment goes to interest; as the balance shrinks, more goes to principal — this is called amortization. The payment is $M = P \times \dfrac{i}{1 - (1 + i)^{-N}}$, where $P$ is the loan amount, $i = r/n$ is the periodic rate, and $N = nt$ is the total number of payments.

The term matters as much as the rate. A longer term lowers each payment but means more payments and far more total interest. Paying a little extra toward principal shortens the loan and cuts the interest you pay over its life.

Worked example

Borrow \$200,000 at a $6\%$ annual rate over 30 years, paid monthly. The periodic rate is $i = 0.06/12 = 0.005$ over $N = 360$ payments, giving a monthly payment of about \$1,199 — and roughly \$231,700 in total interest over the life of the loan, more than the amount borrowed.

Frequently asked questions

How is my monthly payment calculated?

From the loan amount, the periodic interest rate, and the number of payments, using the standard amortization formula $M = P i / (1 - (1+i)^{-N})$.

What is amortization?

The way each payment is split between interest and principal. Early payments are mostly interest; later ones are mostly principal.

Why does a longer term cost more?

Lower payments spread over more periods mean the balance is charged interest for longer, so total interest is higher even though each payment is smaller.

Does paying extra help?

Yes — extra payments go straight to principal, which shortens the loan and reduces the total interest you pay.

Is this calculator free?

Yes — it's free, runs in your browser, and needs no login.

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