The core payment formula
For the United States, India, the United Kingdom, and Australia, the fixed monthly principal and interest payment uses the standard amortization formula:
M = P · r · (1 + r)n / ((1 + r)n − 1)
Here P is the loan amount, r is the periodic interest rate, and n is the total number of payments. For a monthly loan, r is the annual rate divided by 12 and n is the number of years times 12. When the rate is zero, the payment is simply the loan divided by the number of payments.
Amortization and the schedule
We build the schedule one payment at a time. Each month the interest is the current balance times the periodic rate, the scheduled principal is the payment minus that interest, and any extra you enter is applied straight to principal. The balance carries forward until it reaches zero. The interest shown in the results is the exact sum of the interest across every payment, not an approximation.
PMI and its removal
Private mortgage insurance applies when the down payment is under 20%. We estimate it as an annual percentage of the original loan, charged monthly. We remove it the month your balance first reaches 80% of the original home value, which is the point most lenders allow cancellation on request. Federal law also requires automatic termination at 78% based on the original schedule; we use the 80% equity point because it is the threshold borrowers can act on, and we state the removal month in the results.
Extra payments and biweekly schedules
Extra monthly, annual, or one-time amounts are added to principal in the month they occur, and the schedule shortens accordingly. For biweekly, we model the industry-standard behaviour of 26 half-payments a year, which equals 13 monthly payments instead of 12. We implement this as one extra full payment spread evenly across the year, then compare the result against a plain monthly schedule to report the interest and time saved.
Canada: semi-annual compounding
Canadian fixed-rate mortgages compound interest semi-annually by law, not monthly. To convert a quoted annual rate into the effective monthly rate we use:
rmonthly = (1 + annual ÷ 2)1/6 − 1
We then apply the same payment formula. This produces a slightly lower payment than dividing the annual rate by twelve, and it matches how Canadian lenders actually compute the figure. Variable-rate Canadian mortgages compound monthly, in which case the standard monthly conversion applies.
India: reducing-balance EMI
Indian home loans use reducing-balance interest, which is mathematically identical to the standard monthly formula above: interest each month is charged only on the outstanding principal. We present amounts in rupees and note that most Indian rates float with the RBI repo rate. Prepayment is applied directly to principal, with no penalty for individual floating-rate borrowers.
Defaults and where they come from
- Interest rate: the weekly US average from the Freddie Mac Primary Mortgage Market Survey, refreshed every week.
- Property tax: 1.1% of home value per year, near the US effective average, editable to your county.
- Homeowners insurance: about $1,800 per year, a typical US premium.
- PMI: 0.55% of the loan per year, within the common 0.5% to 1.5% range.
Every default is a starting point, not a fixed assumption. The whole point is that you replace them with your own numbers. Full citations are on the sources page.
What we do not do
We do not personalise rates to you, quote lender products, or account for points, closing costs, or credit-based pricing. This is an estimator to help you plan, not a loan offer. See our disclaimer.