Loan Payment Calculator

How a repayment is built

Every repayment does two jobs. First it pays the interest that has accrued on the balance since the last payment. Whatever is left reduces the balance itself. Because interest is charged on the balance, and the balance falls slowly at first, the early years of a long loan are mostly interest and only a little principal.

The payment is the amount that clears both interest and principal in exactly the number of payments agreed, no more and no less. In notation: payment = principal × monthly rate ÷ (1 − (1 + monthly rate)^−payments). The monthly rate is the annual rate divided by twelve, which is the convention lenders use even though it is not quite the mathematically exact equivalent.

Payment

Principal × r ÷ (1 − (1 + r)^−n)

r

Annual rate ÷ 12

n

Years × 12

Because the split changes every month while the payment stays the same, a repayment schedule is called an amortisation schedule. Interest is concentrated at the front, principal at the back.

What actually moves the number

Three inputs decide the payment: how much you borrow, the rate, and the term. The first two act in proportion, the third does not, which is why stretching a loan looks cheaper per month than it really is.

A longer term always lowers the payment and almost always raises the total interest, because you rent the money for longer. The trade is liquidity against cost. A lower rate does both at once, which is why a rate comparison is worth more than a term tweak.

• A 0.5 percentage point lower rate on a $400,000 loan saves roughly $120 a month at the start of a 30-year term.
• Extra repayments go straight to principal and shorten the term without changing the contracted payment.
• A larger deposit reduces principal one-for-one, and also reduces the interest charged from day one.

What the result leaves out

This is the repayment on the loan itself. It does not include establishment fees, ongoing account fees, lender mortgage insurance, stamp duty, or the cost of insuring the asset. On a home loan those can add meaningfully to the first year, and on a small personal loan a fee can rival a month of interest.

It also assumes a fixed rate for the whole term. A variable loan re-prices whenever the lender moves, so the honest use of a fixed-rate figure is as a starting point: run it at your current rate and at a rate one or two points higher to see what a rise would do to the same household budget.

General information only. Lenders assess serviceability, fees and credit history, so an approval will not match a calculator figure exactly.

What each input means

The calculator asks for 3 pieces of information. Every field is validated before the maths runs, so an impossible value is refused rather than quietly producing a wrong answer.

A worked example using the default inputs

With loan amount of 30000, annual interest rate of 8.9 %, term of 5 years, the calculator returns $621.30 per month.

The same arithmetic runs whatever you type into the form above, so you can reproduce any figure by matching the inputs listed here.

How this is calculated

M = P × i ÷ (1 − (1 + i)^−n). A shorter term raises the payment but cuts total interest.

Working values are kept at full precision and rounded only for display. Impossible dates, zero denominators, negative amounts where they make no sense, and out-of-range values are rejected before any result is shown.

The methods behind these money tools

Almost everything in this section is one of six calculations. Once you know which one a tool is running, the result stops being a black box: you can check it roughly on paper, and you can see which input is doing the work.

Two conventions matter more than any formula. First, the rate and the period must match: a 6% annual rate over monthly payments is 0.5% per month and 360 periods, not 6% per period. Second, money paid later is worth less than money paid now, which is why an amortising loan charges interest on the opening balance of each period rather than on the average balance.

Nominal and real returns are different things. A 7% return with 3% inflation buys roughly 3.9% more each year, not 7%: real rate ≈ (1 + nominal) ÷ (1 + inflation) − 1.

Two worked examples from this section

These scenarios use the same arithmetic as the tools above, so you can follow the numbers from input to result and then repeat them with your own figures.

A 30-year mortgage of $600,000 at 6.1%

The monthly rate is 6.1% ÷ 12 ≈ 0.5083% and there are 360 payments. Feeding those into the amortising payment formula gives a fixed instalment of about $3,636.

Monthly principal and interest

≈ $3,636

Total repaid over 30 years

≈ $1,308,900

Interest paid in total

≈ $708,900

Share of the total that is interest

≈ 54%

Notice that more than half of everything paid is interest. That is the single most useful fact a mortgage calculator produces, and it is why a small change in rate or term moves the total so much more than it moves the monthly figure.

Adding and removing 10% GST on $250

Adding tax is a multiplication; removing it is a division by the same factor, never a subtraction of the same percentage. Subtracting 10% from a GST-inclusive price gives the wrong answer because the tax was charged on the smaller, exclusive amount.

$250 plus 10% GST

$275.00

GST component

$25.00

$275 with GST removed (275 ÷ 1.1)

$250.00

The common mistake (275 − 10%)

$247.50 — too low

The same split works for any rate: divide by one plus the rate to go backwards. For 15% VAT, divide by 1.15; for 18% GST, divide by 1.18.

Assumptions behind every finance figure

Results are computed in exact arithmetic and only rounded for display, so a payment shown as $2,413.65 comes from the unrounded monthly rate rather than from a rounded one. Where a calculator compounds, it compounds at the frequency you choose; where it amortises, it assumes payments land at the end of each period unless the tool says otherwise.

Tax and contribution rates are the legislated rates for the tax year noted in each tool. They change, sometimes retrospectively, and none of these tools can see your personal circumstances: deductions, offsets, salary sacrifice, HELP or student loan balances, private health cover, investment losses, provincial or state tax, and treaty arrangements are all outside the model.

• Lenders and tax offices round differently from us, and they use daily interest, fees and assessment rules that a formula cannot reproduce. Expect small differences from an official statement.
• Nominal returns are not real returns. A 7% return with 3% inflation buys about 3.9% more each year, not 7%.
• Every figure is a planning estimate. For a decision with money at stake, confirm it with the lender, the tax office or a licensed adviser.

Sources and further reading

• ASIC Moneysmart: home loans
• Reserve Bank of Australia: interest rates
• Australian Taxation Office: tax rates and codes
• Moneysmart (ASIC): budgeting and borrowing