The payment on a typical home purchase
This calculator covers the principal and interest element of a home mortgage — the portion that goes to the lender and eventually to your own equity.
It is the largest single line in most household budgets, and the one that lenders test hardest before approving. The figures below are what that test operates on.
The formula behind the number
An amortising loan is repaid in equal instalments. Each one covers the interest that accrued since the last payment, and whatever is left reduces the balance. The instalment that brings the balance to exactly zero on the final payment is:
Here P is the amount borrowed, i is the monthly rate (the annual rate divided by 12) and n is the number of payments. Nothing else enters the calculation, which is why two lenders quoting the same three inputs must arrive at the same instalment.
Worked example: $360,000 at 6.5% over 30 years
The calculator opens on this scenario, so you can follow every step:
- Amount borrowed: $360,000
- Annual rate: 6.5%, so the monthly rate is 6.5 ÷ 12 = 0.5417%
- Term: 30 years, so n = 30 × 12 = 360 payments
Paying $2,275.44 every month for 360 months comes to $819,160. Subtract the $360,000 you actually borrowed and the cost of the credit is $459,160, or 128% of the sum borrowed.
Where each payment goes
The instalment never changes, but its composition does. The first payment carries $1,950.00 of interest and only $325.44 of principal. By payment 180 the split has moved to $1,419.54 interest against $855.91 principal.
| Payment | Instalment | Interest | Principal | Balance |
|---|---|---|---|---|
| 1 | $2,275.44 | $1,950.00 | $325.44 | $359,675 |
| 2 | $2,275.44 | $1,948.24 | $327.21 | $359,347 |
| 3 | $2,275.44 | $1,946.46 | $328.98 | $359,018 |
| 180 | $2,275.44 | $1,419.54 | $855.91 | $261,213 |
| 360 | $2,275.44 | $12.26 | $2,263.19 | $0.00 |
Equity builds slowly at first. If you expect to move within five years, check the balance column against your likely sale price before assuming you will walk away with the deposit intact.
What moves the answer most
Two levers change the total, and they do not pull with equal force.
Add one percentage point to the rate and the instalment goes from $2,275.44 to $2,517.17, which is $87,022 more over the full term. Cut 5 years off the term instead and the instalment rises to $2,430.75, but total interest falls from $459,160 to $369,224. Half a point on the rate matters more over thirty years than most buyers assume, and it is negotiable in a way the purchase price often is not.
What this calculator leaves out
Property tax, insurance, mortgage insurance and any association fee sit on top of this figure. Together they commonly add twenty to thirty percent to the monthly cost.
Related calculators
- With taxes and insurance — the full monthly outlay
- Affordability calculator — the maximum price your income supports
- 28/36 rule calculator — the ratios underwriters apply