Mortgage Calculator

What this calculator answers

A mortgage calculator exists to answer two questions a listing never tells you: what the house costs every month, and how much of the total price is interest rather than house. Buyers use it to work out what they can carry; existing owners use it to test whether an extra payment each month is worth making; and anyone comparing a 15-year term against a 30-year one needs it because the difference is not intuitive — halving the term does not double the payment.

A worked example: $300,000 at 6% over 30 years

Put in a $300,000 price with $60,000 down and you are borrowing $240,000. At 6% over 30 years on the US convention, the principal-and-interest payment is $1,438.92 a month. Over the full term you pay $518,011.65, of which $278,011.65 is interest — more than the amount borrowed.

The first payment is the one that surprises people. Interest for month one is $240,000 × 0.5% = $1,200.00, so only $238.92 of that $1,438.92 goes to the balance. By the end of year one you have paid $14,319.83 in interest and $2,947.23 in principal, leaving $237,052.77 owed.

Add $200 a month and the picture changes sharply: the loan clears in 265 months instead of 360 — 7 years 11 months early — and total interest falls to $192,926.32, a saving of $85,085.34. Add the sample $3,600 property tax and $1,200 insurance and the monthly figure at the top becomes $1,838.92, because those are billed on the house, not the loan.

Fifteen years does not cost twice as much a month

The short-term-against-long-term question is the one arithmetic answers best, because the intuition is reliably wrong in a particular direction. Halving the term does not double the payment. Hold the same $240,000 at 6% and change nothing but the number of years.

The fifteen-year payment is 41% higher than the thirty-year one rather than 100% higher, and it takes $153,466 off the interest bill. The reason it is nonetheless out of reach for many buyers is that lending is underwritten against the payment and not against the total: $586 a month more is $586 a month a lender has to find in your income today, whatever it saves across fifteen years you would not be paying at all.

What a rate quote is worth, in money

Shopping lenders is tedious, and it is the best-paid hour in the whole purchase. Same $240,000, same thirty years, nothing changed but the rate on the offer.

Half a point is worth $78 a month here, and $28,095 across the term. Notice as well that the interest column climbs faster than the rate does: 7% is two-fifths higher than 5%, and its interest bill is half again as large. That is compounding seen from the borrower’s side — a higher rate leaves less of each payment for the balance, so the balance the next month’s interest is charged on is higher too.

The formula, stated plainly

The scheduled payment comes from the standard annuity formula: payment = P × r ÷ (1 − (1 + r)^−n), where P is the amount borrowed, n is the number of monthly payments and r is the interest rate for one month. Each month the calculator charges interest of balance × r, applies whatever the payment leaves over to the balance, and repeats until the balance reaches zero.

US monthly versus Canadian semi-annual compounding

A US mortgage quotes a nominal annual rate that is simply divided by twelve, so 6% means 0.5% a month. Canadian mortgages are conventionally quoted and calculated on semi-annual compounding, so a quoted 6% means 3% every six months, and the equivalent monthly rate is (1 + 0.06 ÷ 2)^(1÷6) − 1 = 0.4938622% — slightly less than 0.5%.

That convention comes from a disclosure rule rather than a cap on compounding. Section 6 of Canada’s Interest Act says that where a mortgage on real property makes principal and interest payable in blended instalments — which is what an ordinary amortized mortgage does — no interest is recoverable at all unless the mortgage document states the principal and the rate of interest “calculated yearly or half-yearly, not in advance”. Half-yearly is the more favourable of the two a lender may state, so it is what Canadian mortgages are written on, and the Bank of Canada describes payments as calculated assuming monthly payments and semi-annual compounding. The law governs what the document must say; the semi-annual convention is the practice that follows from it.

On the same $240,000 loan that gap is worth $11.34 a month: $1,427.58 on the Canadian convention against $1,438.92 on the US one, and $273,927.44 of interest against $278,011.65. Small per payment, $4,084 across the term. Use the setting that matches where the loan was written; using the US formula on a Canadian mortgage makes every figure on the page slightly wrong in the same direction.

What is deliberately left out

The projection assumes a fixed rate for the whole term and a payment made on schedule every month. It does not model a variable or adjustable rate, a rate reset at renewal, mortgage insurance (PMI or CMHC), HOA or condo fees, closing costs, or the tax deductibility of interest in jurisdictions that allow it.