Thirty years of a mortgage, month by month
Over a thirty-year term the amortisation curve is at its most extreme. Understanding where you sit on it explains why refinancing, selling or overpaying produce such different results depending on timing.
The instalment stays the same for three hundred and sixty months. The composition changes completely, and the table below marks the turning points.
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: $300,000 at 6% over 30 years
The calculator opens on this scenario, so you can follow every step:
- Amount borrowed: $300,000
- Annual rate: 6%, so the monthly rate is 6 ÷ 12 = 0.5000%
- Term: 30 years, so n = 30 × 12 = 360 payments
Paying $1,798.65 every month for 360 months comes to $647,515. Subtract the $300,000 you actually borrowed and the cost of the credit is $347,515, or 116% of the sum borrowed.
Where each payment goes
The instalment never changes, but its composition does. The first payment carries $1,500.00 of interest and only $298.65 of principal. By payment 180 the split has moved to $1,069.38 interest against $729.27 principal.
| Payment | Instalment | Interest | Principal | Balance |
|---|---|---|---|---|
| 1 | $1,798.65 | $1,500.00 | $298.65 | $299,701 |
| 2 | $1,798.65 | $1,498.51 | $300.14 | $299,401 |
| 3 | $1,798.65 | $1,497.01 | $301.65 | $299,100 |
| 180 | $1,798.65 | $1,069.38 | $729.27 | $213,147 |
| 360 | $1,798.65 | $8.95 | $1,789.70 | $0.00 |
The halfway point in time is nowhere near the halfway point in debt. Most borrowers reach half the balance repaid only in the third decade.
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 $1,798.65 to $1,995.91, which is $71,012 more over the full term. Cut 5 years off the term instead and the instalment rises to $1,932.90, but total interest falls from $347,515 to $279,871. This asymmetry is why overpayments made in the first years are worth several times the same amount paid in the last years.
What this calculator leaves out
Tax, insurance and service charges are excluded, as is any rate change. Refinancing restarts the schedule from the beginning of the curve, which is a cost that rarely appears in refinancing comparisons.
Related calculators
- Full mortgage calculator — with tax, insurance and overpayments
- Refinance calculator — whether restarting the curve is worth it
- Loan balance calculator — the outstanding figure at any point