Mortgage Calculator, Explained

After reading this you can compute a mortgage payment by hand, split any payment into interest and principal, read an amortization schedule, and spot the assumptions that make the printed number wrong.

What a mortgage calculator does

A repayment mortgage is a loan you pay off in equal monthly installments. Each payment covers the interest owed that month, and whatever is left reduces the balance. Early on, most of the payment is interest. Late in the term, most of it is principal. The calculator finds the single payment that clears the balance to exactly zero after the last month.

Here is the hook. Borrow 240000 at 6.5% for 30 years and the monthly principal-and-interest payment is about 1516.96. Over 360 months you pay 546,105 in total, of which 306,105 is interest. You pay more in interest than the entire cash price of a 300000 house you bought with a 20% down payment.

When to use it, and when not

Use this tool to compare loan offers, to see how rate and term change the payment, and to build a full month-by-month schedule. It also adds property tax and home insurance so you see a realistic total monthly cost, not just the loan portion.

Do not use it to decide how much house you can afford. That question depends on your income and other debts, so start with the Home Affordability Calculator. If you are choosing between renting and owning, the Rent vs Buy Calculator weighs the long-run costs of both. This calculator assumes a fixed rate for the whole term. If your loan has a variable rate, the payment shown is only correct until the rate resets.

The payment here covers principal, interest, tax and insurance. It does not include private mortgage insurance (charged on many low-deposit loans), HOA fees, or closing costs. Add those separately when you budget.

The formula and why it works

Let L be the amount borrowed, i the monthly interest rate, and n the number of monthly payments. The monthly principal-and-interest payment M is:

M = L \cdot \frac{i(1+i)^n}{(1+i)^n - 1}

Here L is the home price minus the down payment. The monthly rate is the annual rate divided by 12, so i = 0.065 / 12 \approx 0.005417. The term count is years times 12, so a 30-year loan has n = 360.

The formula comes from one idea: the present value of all future payments must equal the amount borrowed. A payment of M made k months from now is worth M / (1+i)^k today. Sum that geometric series from k = 1 to n, set it equal to L, and solve for M. The fraction above is what falls out.

When the rate is zero the formula divides by zero, so handle that case separately: with i = 0 you simply repay M = L / n.

A worked example with the demo numbers

Price 300000, 20% down, 6.5% for 30 years

Down payment: 0.20 × 300000 = 60000. Loan amount L = 300000 - 60000 = 240000.
Monthly rate: i = 0.065 / 12 = 0.0054167. Payment count n = 360.
Compound factor: (1+i)^n = 1.0054167^{360} \approx 6.9917.
Apply the formula: M = 240000 \cdot \frac{0.0054167 \times 6.9917}{6.9917 - 1} \approx 1516.96.
Property tax: 1% × 300000 = 3000 per year, or 250.00 per month. Insurance: 1500 / 12 = 125.00 per month.
Total monthly cost: 1516.96 + 250.00 + 125.00 = 1891.96.

Loan-to-value (LTV) is the loan divided by the price: 240000 / 300000 = 0.80, or 80%. Lenders watch this number closely, and many charge extra insurance above 80%. The Down Payment & LTV Calculator works this angle directly.

How the balance falls over time

Each month the interest charged is the current balance times i. In month 1 that is 240000 \times 0.0054167 = 1300.00. Your payment is 1516.96, so only 1516.96 - 1300.00 = 216.96 reduces the balance. In month 360 the interest is tiny and almost the whole payment is principal.

The balance therefore does not fall in a straight line. It curves down slowly at first and steeply near the end. The chart below plots the demo loan's balance across all 360 months.

The balance barely moves in the first few years, then drops fast near the end as more of each payment goes to principal.

The yearly schedule the tool prints shows the same story in numbers: interest paid, principal paid, and closing balance for each year. After year 10 you still owe 203,140 of the original 240000, having repaid only 36,860 of principal while paying far more than that in interest.

Reading the results without fooling yourself

Principal and interest (P&I): The loan-only payment from the formula. It never changes on a fixed-rate loan.
Total monthly cost: P&I plus monthly tax and insurance. This is closer to what leaves your account, but still excludes PMI, HOA and maintenance.
Total interest: The sum of every month's interest. For the demo loan that is about 306,105 over 30 years.
LTV: Loan divided by price. Lower is safer for the lender and often cheaper for you.

Watch how sensitive the payment is to the rate. At 5.5% the demo payment is about 1362.69. At 7.5% it is about 1678.11. A two-point swing in rate moves the payment by 315 a month, or 113,400 over the full term. The interactive below lets you feel that.

Common mistakes

Do not divide the annual rate by 12 in your head and forget to compound. Interest at 6.5% per year is not the same as adding 0.5417% once. Because interest compounds monthly, the effective annual cost is (1.0054167)^{12} - 1 \approx 6.70\%, slightly above the stated rate.

Three more traps catch people often. First, confusing price with loan amount: the formula uses the amount borrowed, not the price, so the down payment must be subtracted first. Second, forgetting that tax and insurance are not part of the loan and do not shrink as you repay; tax often rises as the home is reassessed. Third, treating the total interest figure as fixed. Overpaying even a little cuts it sharply, because every extra dollar of principal stops accruing interest for the rest of the term.

To see how much overpaying saves, use the Mortgage Extra Payment Calculator or the Biweekly Mortgage Calculator. If you already hold a loan and a lower rate appears, the Mortgage Refinance Calculator shows the break-even point after fees.

Related tools

These pages handle the questions this calculator deliberately leaves out. The Rent Affordability Calculator applies the 30% rule if you are renting instead. The Prorated Rent Calculator handles a partial first month. When comparing properties by size, the Price per Square Meter Calculator puts them on one scale.

The principal borrowed is the same in all three cases. Total interest roughly doubles when you stretch from 15 years to 30.

Frequently asked questions

Why is my real payment higher than the calculator shows?

The P&I figure covers only the loan. Your lender may add private mortgage insurance if your LTV is above 80%, plus HOA dues and any escrow shortfalls. Tax and insurance shown here are estimates from your inputs; the actual bills can differ.

Does a bigger down payment always save money?

It lowers the loan, so it lowers both the payment and total interest. On the demo loan, putting 25% down instead of 20% cuts the loan to 225000 and the payment to about 1422.15. The trade-off is less cash left for emergencies, so it is not automatically the right choice.

What is the difference between the interest rate and the APR?

The interest rate drives the formula. The APR folds in certain fees and is usually a little higher. This tool uses the plain interest rate, so compare offers on rate here and check the APR separately for the true cost including fees.

How can I pay less total interest?

Shorten the term, get a lower rate, or overpay principal. On the demo loan, switching from 30 to 15 years cuts total interest from about 306,105 to about 136,349, though the monthly payment rises to about 2090.83.

Is this financial advice?

No. It is an educational estimate to help you understand the math. Talk to a qualified adviser before making a decision about a mortgage.

Try it yourself in the tool