The Home Loan Repayment Formula, Worked Step by Step
ADS Team
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July 20, 2026
about 2 months ago
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In short: Australian lenders calculate your repayment with the amortisation formula P = r × PV ÷ (1 − (1 + r)−n), where PV is the amount borrowed, r is the annual interest rate divided by 12, and n is the number of monthly payments. On a $750,000 loan at 6.5% over 30 years that produces a repayment of $4,740 a month.
Key takeaways
- Every repayment is the same size, but its split between interest and principal changes every month.
- r is the monthly rate — the annual rate divided by 12, not the annual rate itself.
- On a $750,000 loan at 6.5% over 30 years, the repayment is $4,740 a month and total interest over the full term is about $956,000.
- Halving the term to 15 years raises the repayment to about $6,534 but cuts total interest by roughly two thirds.
What are the four inputs?
Only four numbers matter, and every lender uses the same four:
- PV — the present value, meaning the amount you actually borrow after your deposit.
- r — the periodic interest rate. For monthly repayments this is the annual rate ÷ 12. At 6.5% that is 0.065 ÷ 12 = 0.00541667.
- n — the number of repayments. A 30-year loan paid monthly is 30 × 12 = 360.
- P — the repayment the formula returns.
The most common mistake is putting the annual rate into r. That inflates the result by roughly a factor of twelve and is usually why a hand calculation disagrees with a lender's number.
Working the formula on a $750,000 loan
Take a $750,000 loan at 6.5% over 30 years.
- Convert the rate: r = 0.065 ÷ 12 = 0.00541667
- Count the payments: n = 30 × 12 = 360
- Compute the discount factor: (1 + 0.00541667)−360 = 0.14301
- Subtract from one: 1 − 0.14301 = 0.85699
- Multiply rate by principal: 0.00541667 × 750,000 = 4,062.50
- Divide: 4,062.50 ÷ 0.85699 = $4,740
Over 360 payments you repay about $1,706,000 in total, of which roughly $956,000 is interest — more than the amount borrowed.
How does the repayment change with loan size?
The formula is linear in the principal, so once you have the repayment for one loan size you can scale it. At 6.5% over 30 years:
| Loan amount | Monthly repayment | Total interest over 30 years |
|---|---|---|
| $300,000 | $1,896 | $382,600 |
| $500,000 | $3,160 | $637,700 |
| $650,000 | $4,108 | $829,000 |
| $750,000 | $4,740 | $956,500 |
| $1,000,000 | $6,320 | $1,275,300 |
The useful shortcut: at 6.5% over 30 years, every $100,000 borrowed costs about $632 a month.
Why is the term so powerful?
Shortening the term raises the repayment far less than proportionally, because you stop paying interest for the years you removed. On the same $750,000 at 6.5%:
| Term | Monthly repayment | Total interest |
|---|---|---|
| 30 years | $4,740 | $956,500 |
| 25 years | $5,063 | $768,900 |
| 20 years | $5,592 | $592,100 |
| 15 years | $6,534 | $426,200 |
Cutting from 30 years to 20 costs $852 a month but saves about $364,000 in interest.
Frequently asked questions
Why does my lender's repayment differ from the formula by a few dollars?
Most Australian lenders accrue interest daily on the outstanding balance and charge it monthly, while the formula assumes clean monthly compounding. Month length and the timing of your payment date produce small differences, usually only a few dollars.
Does the formula work for interest-only loans?
No. During an interest-only period the repayment is simply the balance × the annual rate ÷ 12, with no principal component. On $750,000 at 6.5% that is $4,063 a month. The amortisation formula applies again once the loan reverts to principal and interest, but over the shortened remaining term.
What rate should I use if I want to be conservative?
Lenders assess you at your rate plus APRA's serviceability buffer, held at 3.0 percentage points. Running the formula at your rate plus 3% shows the repayment you are being tested against, which in mid-2026 is around 9.25% to 9.5% for most borrowers.
Sources
- Cash rate target and interest rate statistics — Reserve Bank of Australia
- Serviceability buffer guidance, APG 223 — APRA
Rates checked as at 2 September 2026. Interest rates, lender policies and government schemes change frequently. Figures in this article are illustrative and were accurate at the date shown.
General advice warning: This article contains general information only. It does not take into account your objectives, financial situation or needs, and it is not personal credit or financial advice. Consider whether it is appropriate for you and seek advice from a licensed credit representative before acting.
Any interest rate shown is an example only and is not an offer of credit. Where a rate is quoted, the applicable comparison rate is available from the relevant lender and should be considered alongside it.
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