How to calculate mortgage repayment, step by step
To calculate mortgage repayment, work out the monthly payment from the loan, the rate and the term, then multiply the payment by the number of months to find the total repaid, and subtract the loan to find the total interest. The monthly payment is the loan times the monthly rate, divided by one minus one plus the monthly rate to the power of minus the months — the standard amortization formula. On the worked example below, a $400,000 loan at 6.50% over 30 years costs $2,528.27 a month, $910,177.95 in all, of which $510,177.95 is interest, and the loan is paid off in October 2056. The whole method is four steps, and the only decision in it is whether to pay extra — the extra payment is the lever that changes everything.
The worked example: $400,000, 6.50%, 30 years
Step 1 — write down the loan, the rate and the term: $400,000, 6.50% a year, 30 years, which is 360 months. Step 2 — work out the monthly rate: 6.50% divided by 12 is 0.5417% a month. Step 3 — work out the monthly payment: $400,000 times the monthly rate, divided by one minus one plus the monthly rate to the power of minus 360, is $2,528.27. Step 4 — work out the total repaid: $2,528.27 times 360 months is $910,177.95. Step 5 — work out the total interest: $910,177.95 minus $400,000 is $510,177.95. Step 6 — work out the payoff date: October 2026 plus 360 months is October 2056. That is the whole calculation, and the mortgage-repayment-calculator does it for any loan: a $300,000 loan at the same rate and term costs $1,896.20 a month and $382,633.47 of interest, and a 15-year term on $400,000 costs $3,484.43 a month and $227,197.30 of interest.
What mortgage repayment is
Mortgage repayment is the total amount a borrower pays back over the life of a mortgage: the loan itself plus the interest charged on it. It has three pieces: the loan amount, which is the money borrowed; the interest rate, which is the price of borrowing it, charged each month on the balance still owed; and the term, which is how many years the loan runs. The monthly payment is fixed for a fixed-rate loan, and each payment is split into interest and principal — early payments are mostly interest, because the balance is at its biggest, and late payments are mostly principal. The total repaid is the payment times the months, and the total interest is the total repaid minus the loan. The payoff date is the month the last payment is made.
What extra payments save
An extra payment goes straight to principal, so it cuts the balance the interest is charged on, and the saving compounds. On the worked example, an extra $200 a month ends the loan in 293 months instead of 360 — March 2051 instead of October 2056, 67 months sooner — and saves about $111,900 of interest. An extra $500 a month ends it in 233 months — March 2046, 127 months sooner — and saves about $205,600. Even $5,000 a month ends it in 63 months, January 2032, with only $72,992.15 of interest. The payment itself never changes — the loan just ends sooner. To pay the loan off in 20 years instead of 30 takes about $454 a month extra, on top of the $2,528.27 payment.
15 years against 30 years
The term is the second lever. A 15-year term on $400,000 at 6.50% costs $3,484.43 a month — $956.16 more than the 30-year payment — but the total interest is $227,197.30, less than half the 30-year $510,177.95. A 20-year term sits between them: $2,982.29 a month and $315,750.21 of interest. The shorter term is the cheaper loan by a wide margin; the longer term is the cheaper month. A rate of 7.50% instead of 6.50% pushes the 30-year payment to $2,796.86 a month and the total interest to $606,868.89, which is why the rate you lock matters more than almost anything else in the loan.
How to work backwards from a payment budget
To find the biggest loan a budget allows, work the formula backwards — or use the reverses in the mortgage-repayment-calculator. For a $2,500 a month payment at 6.50% over 30 years, the loan can be about $395,500. The rate works backwards too: a rate of about 6.39% keeps the payment at $2,500 a month on a $400,000 loan over 30 years. And the extra payment works backwards as well: about $454 a month extra pays the loan off in 20 years. Working backwards is how a buyer sets a budget before the house hunt starts, instead of finding out after the offer that the payment does not fit.
Common mistakes
The first mistake is looking only at the monthly payment: a $2,528.27 payment sounds manageable, but the loan costs $910,177.95 in all, and $510,177.95 of that is interest — more than the loan itself. The second is forgetting that the payment is principal and interest only: property tax, homeowner's insurance, PMI and HOA fees are on top, and they can add hundreds a month. The third is assuming the rate stays put: the formula assumes a fixed rate, but an adjustable-rate loan can reset higher and the payment with it. The fourth is paying extra without checking that it goes to principal — most modern mortgages apply it that way, but check before you pay. And the fifth is rounding the months: a 30-year loan is 360 payments, and the last one is adjusted so the balance lands exactly on zero — the payoff date is October 2056, not a month later.
A quick check you can do in your head
You can sanity-check any mortgage repayment without a calculator. First, the pieces must add up: $2,528.27 times 360 is $910,177.95, and $910,177.95 minus $400,000 is $510,177.95. Second, the payment must rise with the loan and the rate and fall with the term: a $300,000 loan is $1,896.20 a month, a 7.50% rate is $2,796.86, and a 15-year term is $3,484.43. Third, extra payments must shorten the loan and cut the interest: $200 extra saves about $111,900 and 67 months, and $500 extra saves about $205,600 and 127 months. If a calculator breaks any of these checks, the number is wrong — run your numbers through the mortgage-repayment-calculator and compare them with the worked example above.