Compound Interest Calculator

The mechanism is interest on interest

Simple interest is charged once on the original amount and never changes. Compound interest is charged on the balance, which now includes interest already credited, so each period earns a little more than the last. The gap between the two starts as rounding and ends up as the largest part of the result.

$10,000 at 5% a year for ten years pays $5,000 under simple interest. Under annual compounding it reaches $16,289, because the interest credited in year one earns interest in year two. Nothing about the rate changed; only the base it applies to did.

Formula

A = P × (1 + r ÷ n)^(n × t)

P

Starting principal

r

Annual rate as a decimal

n

Compounding periods per year

t

Years

Why compounding frequency matters less than rate

Compounding more often credits interest earlier, so the same nominal rate produces a slightly higher effective return. The effect is real but small compared with the rate itself: 5% compounded monthly is 5.12% effective, while 5% compounded annually is exactly 5%.

The practical reading: frequency is a tiebreaker between two otherwise identical products, not a reason to choose one. A 40 basis point difference in the headline rate outweighs the whole frequency effect.

Time does more work than anything else

Growth is exponential in time, which is why the last years of a long horizon contribute more than the first. As a quick estimate, a balance doubles in roughly 72 ÷ rate years: about 14 years at 5%, about 9 years at 8%. The rule is approximate but it is close enough to compare scenarios in your head.

• Run the same figures at a conservative and an optimistic rate, and plan on the conservative one.
• Check the fee load: a 1% annual fee is functionally a 1% lower rate, compounded for the whole horizon.
• Ignore inflation in the nominal figure, or model a real return instead, but never mix the two in one comparison.

General information only. Investment returns vary and are not guaranteed, and tax on earnings depends on your circumstances.

What each input means

The calculator asks for 5 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 starting balance of 10000, annual interest rate of 5.5 %, years invested of 10 years, compounding of Monthly, monthly contribution of 200, the calculator returns $49,212.28.

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

Lump sum: A = P(1 + r/n)^(nt). Contributions use the future-value-of-an-annuity formula at the monthly rate: A = c × ((1 + i)^m − 1) ÷ i.

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