Mortgage Calculator
Work out the monthly repayment on a mortgage, the total you will repay, and how much of it is interest.
The formula
A repayment mortgage is an annuity: you pay the same amount every month, and each payment covers that month’s interest first, with the remainder reducing the balance. The payment that clears the loan exactly at the end of the term is
M = P × r ÷ (1 − (1 + r)^−n)
where
- P is the amount borrowed,
- r is the monthly interest rate, the annual rate divided by 12, then by 100,
- n is the number of monthly payments, which is the term in years times 12.
At a 0% rate that expression divides by zero, and the answer is simply P ÷ n.
Worked example
Borrow 250,000 at 5.5% a year over 25 years.
r = 5.5 ÷ 100 ÷ 12 = 0.00458333…n = 25 × 12 = 300(1 + r)^−n = 1.00458333…^−300 = 0.253566…M = 250000 × 0.00458333… ÷ (1 − 0.253566…) = 1145.833… ÷ 0.746434… = 1535.22
So about 1,535.22 a month. Over 300 payments that is 460,566 repaid in total, of which 210,566 is interest, 84.2% of the sum borrowed, paid again on top of it.
Keep the full precision through the intermediate steps. Rounding r to five
decimal places before the final division shifts the answer by roughly 9 cents a
month, which compounds to about 27 over the full term.
What this does not include
The figure above is principal and interest only. A real mortgage payment often also carries buildings insurance, property tax, and mortgage insurance, and a fixed rate that later reverts to a variable one will change the payment partway through the term. Treat the result as the cost of the borrowing itself, not the full monthly outgoing.