Mortgage Calculator

Principal and interest is only part of the payment

The loan itself produces a level payment covering interest and principal. What a lender quotes as a monthly payment usually also includes property tax and home insurance, collected monthly and held until the bills fall due, and sometimes mortgage insurance and a HOA or service charge.

amount borrowed = home price − down paymentprincipal and interest = amount × r ÷ (1 − (1 + r)^−n)total monthly = principal and interest + tax/12 + insurance/12 + HOA + mortgage insurance

Separating the two makes it obvious which part of the payment is the loan and which part would exist whatever the financing looked like. Tax and insurance do not disappear when a mortgage is paid off.

How to read the amortization schedule

Each row of the schedule is one year of payments, counted from your first payment rather than from January. Three figures describe that year:

• Principal is how much the loan went down during the year.
• Interest is what the lender charged for the year. It never reduces what you owe.
• Balance is what you would still owe after the last payment of that year.

Across any full year, principal plus interest equals twelve monthly payments of principal and interest. Down the whole table, the principal column adds up to the amount borrowed and the interest column adds up to the total interest shown with the results. The balance in one row, less the next row’s principal, gives the next row’s balance, so you can check any line against the one above it.

Why the first years are mostly interest

Every month the lender works out interest on whatever is still owed:

interest this month = balance still owed × annual rate ÷ 12principal this month = monthly payment − interest this month

The payment stays the same, so the interest is taken out first and only the remainder goes to the loan. At the start the balance is the full amount borrowed, which makes the interest charge as large as it will ever be. As the balance falls, the charge shrinks and more of the same payment is left for principal, which lowers the balance faster again. The effect compounds slowly and then quickly, which is why the principal column climbs gently for most of the term and steeply at the end.

Two things change the shape. A higher rate makes the monthly interest charge larger, so principal takes longer to catch up. A longer term lowers the payment, so less is left over after interest in the early years. Changing the rate or the term here and watching the first row of the schedule shows both.

If you are comparing the schedule with a lender’s statement, small differences can come from the day your first payment falls due, from interest charged by the day rather than the month, or from escrow changes. This schedule assumes every payment arrives on time and in full at a fixed rate, with nothing added to the balance.

Loan to value, and why it matters to a lender

Loan to value is the amount borrowed divided by the price. A 20% down payment gives 80% loan to value, which is the threshold at which many lenders stop requiring mortgage insurance. The figure shown here uses the purchase price, not an appraisal, and lenders use the lower of the two.

This calculator reports the ratio and stops there. Whether a given ratio qualifies for a particular rate or removes a particular requirement is a lending decision, and lenders differ.

Averaged costs are estimates, not fixed amounts

Property tax is reassessed. Insurance premiums move at renewal. Dividing an annual figure by twelve gives a usable monthly number, but it is an average of a cost that changes, which is why the total payment here is labelled an estimate while principal and interest is exact.

Escrow shortfalls are a common surprise for that reason: when the tax bill rises, the lender recalculates the monthly collection and the payment goes up even though the loan has not changed.

What is left out

Closing costs, points paid to lower the rate, origination and appraisal fees, and anything rolled into the loan balance are all outside this calculation. So are rate changes on an adjustable mortgage, which make every figure beyond the first fixed period provisional, and extra payments, which the mortgage payoff calculator handles.

For the trade-off between a lower rate and the cost of getting it, compare total interest over the term rather than the monthly payment alone. A longer term almost always lowers the payment while raising the total cost.