How we calculate mortgage repayments

The standard annuity formula

Your monthly payment M is the amount that reduces the balance to exactly zero at the end of the term:

M = P × [ i(1+i)ⁿ ] / [ (1+i)ⁿ − 1 ]

where:
  P = loan principal
  n = total number of payments (term × periods per year)
  i = periodic interest rate (see per-country conventions below)

Per-country conventions

Country	Convention	Periodic rate
US	standardMonthly	i = r / 12
UK	standardMonthly	i = r / 12
CA	canadianSemiAnnual	i = (1 + r/2)^(1/6) − 1
AU	standardMonthly	i = r / 12
IE	standardMonthly	i = r / 12
DE	standardMonthly	i = r / 12
NL	standardMonthly	i = r / 12
NZ	standardMonthly	i = r / 12
FR	standardMonthly	i = r / 12
ES	standardMonthly	i = r / 12
SG	standardMonthly	i = r / 12
IN	standardMonthly	i = r / 12

Official test vectors

Every convention is tested against worked examples from official sources. These test vectors are the acceptance criteria for the engine:

FRED MORTGAGE30US — $400,000 @ 6.5% × 30yr monthly (standard annuity)

Source: Freddie Mac Primary Mortgage Market Survey, FRED series MORTGAGE30US

Principal	400,000
Annual rate	6.50%
Term	30 years
Expected payment	2,528.27

Bank of Canada — $500,000 @ 5.0% × 25yr monthly (semi-annual compounding)

Source: Bank of Canada mortgage calculator methodology, Interest Act RSC 1985

Principal	500,000
Annual rate	5.00%
Term	25 years
Expected payment	2,907.59

Bank of England — £300,000 @ 4.5% × 25yr monthly (standard annuity)

Source: Bank of England mortgage repayment guidance

Principal	300,000
Annual rate	4.50%
Term	25 years
Expected payment	1,667.03

RBA — $600,000 @ 6.0% × 30yr monthly (standard annuity)

Source: Reserve Bank of Australia, Statistical Table F6

Principal	600,000
Annual rate	6.00%
Term	30 years
Expected payment	3,597.30