Rates Explained: Mortgages

Do the math yourself

Want to check the numbers yourself? Here's the recipe.

Three things decide your monthly payment: how much you borrow, the interest rate, and how many years you take to pay it all back. Put them into the recipe below and out comes your payment.

$$400,000borrowed+5%5% ratefixed+2525 yearsto pay it all$2,326$2,326a monthcalculator
Example: $400,000 at a 5% fixed rate over 25 years is about $2,326 a month.

The recipe, step by step

  1. How much you borrow = home price − down payment. With less than 20% down, add the insurance fee.
  2. The monthly rate (call it i). Fixed rate: (1 + yearly rate ÷ 2)^(1/6) − 1. That's because the Interest Act requires a mortgage to state its rate worked out yearly or twice a year, not in advance1, and fixed rates are normally worked out twice a year. Variable rate: yearly rate ÷ 12. This site assumes that for variable rates, which is common, but check your own agreement.
  3. Number of payments (n) = years × 12
  4. Monthly payment = amount borrowed × i ÷ (1 − (1 + i)^(−n))
  5. Each month: interest = what you owe × i. The rest of the payment pays down what you owe. Repeat.
The whole formula in one line Fixed rate: Payment = P × [(1 + r÷2)^(1÷6) − 1] ÷ [1 − (1 + r÷2)^(−2 × y)] Variable rate: Payment = P × (r÷12) ÷ [1 − (1 + r÷12)^(−12 × y)]

P = amount borrowed (including any insurance fee) · r = yearly rate as a decimal (4.84% is 0.0484) · y = years

Your numbers. The same recipe, worked through with your numbers. Drawn with your numbers from the calculators: loading….
References
  1. Interest Act, section 6 (Justice Laws)