Compound interest calculator

How compound interest works, and the formula behind it

Simple interest is charged on the original amount, every period, forever. Compound interest is charged on the original amount plus every bit of interest already added. That single difference is the reason a balance curves upwards instead of climbing in a straight line.

Read the exponent slowly, because that is where the whole thing lives. Time sits up in the power so adding years multiplies the result, while the rate sits down in the base and only adds to it. That is why patience beats chasing a slightly better return over any long horizon.

Regular contributions are handled separately. Each one starts compounding from the period it lands in, so a dollar added in year one has nineteen more years of growth ahead of it than the same dollar added in year twenty. The calculator adds each contribution at the end of its period and compounds the balance from there.

Nominal rate against effective annual rate

A rate quoted as 6% a year is a nominal rate, and it is not what you actually earn unless the interest compounds exactly once a year. Compound it more often and each addition starts earning immediately, so the real return is higher than the number advertised.

The effective annual rate is what 6% turns into once the compounding is counted. The arithmetic is (1 + r ÷ n) to the power of n, minus 1. At 6% compounded monthly that is 1.005 to the power of 12 minus 1, or 6.1678%.

Across a decade, moving from annual to daily compounding on that balance is worth $312. It is real money and it is a rounding error next to what an extra five years does. Frequency is the second lever for a reason.

The effective annual rate is the honest basis for comparing two accounts. Two products quoting the same nominal rate are not paying the same thing if one compounds monthly and the other annually, and only the effective rate makes that visible.

Why the first years look disappointing and the last years do the work

Most people give up on compounding in the first few years, because in the first few years it does almost nothing. The curve is nearly flat at the start and it only becomes obvious when there is enough interest in the pile for the interest to matter.

The first five years of that account earn $3,489 in total. The last five earn $15,576. Same money, same rate, nothing changed except how much interest was already sitting there doing the work.

This is also the argument for starting with a small contribution rather than waiting until you can afford a serious one. Years in the market cannot be bought back later, and no contribution you make in year twenty will do what a smaller one did in year one.

Using the interest compounding calculator without fooling yourself

The tool will return a large and cheerful number for any rate you type. Whether that number means anything depends entirely on the inputs, so a few rules on how to set them.

1. 1

   Use a rate you have actually been offered

   Not a hoped-for return, and not a long-run average from somewhere else. The rate that loads is a round example, put there so the tool has something to draw, and it is the first thing you should change.

2. 2

   Match the compounding frequency to the product

   It is stated in the terms and conditions and it is usually monthly or daily. Guessing it wrong changes the effective annual rate, which changes everything downstream.

3. 3

   Set a contribution you will still be making in year five

   A contribution you abandon after eight months does nothing. A smaller one you keep up is worth more than a heroic one you do not, and the tool has no way of knowing which you entered.

4. 4

   Read the total contributed row before the headline

   It tells you how much of the final balance is your own money rather than growth. On $10,000 plus $500 a month at 6% compounded monthly for twenty years, the balance reaches $264,122, of which $130,000 is what you put in.

That example is worth sitting with. Interest accounts for $134,122 of the final balance, slightly more than everything you contributed, and the same $10,000 left alone with no contributions would have reached only $33,102.

Compounding runs against you on a mortgage

The maths that grows a savings balance is the same maths that makes a thirty-year loan cost what it costs. On a debt you are on the other side of it, and the compounding is being applied to money you owe.

An example $600,000 home loan at 6% over 30 years has a monthly repayment of about $3,597 and costs $695,029 in interest across the term. That is more than the house. It is compounding, charged against you every month for three decades.

The useful consequence is that paying a debt down early is compounding put back on your side of the ledger. An extra repayment removes the balance it pays off and every interest charge that balance would have attracted for the rest of the term, which makes it a guaranteed return at your loan rate.

• A guaranteed return at your loan rate, with no market risk and no tax on the gain
• Worth most in the first years of a loan, when the balance and the remaining term are both at their largest
• On that example loan, an extra $200 a month clears it 3 years and 11 months early and saves over $106,000 in interest
• An offset account does the same job while keeping the money available, which our offset account calculator prices
• Our extra repayments calculator runs this properly on your own balance and rate

That is why a mortgage broker has a compound interest calculator on the site at all. Most people meet compounding as a savings idea and then spend thirty years on the wrong end of it without ever making the connection.

Tax and inflation: what an Australian compound interest calculator leaves out

This tool models growth and nothing else. Two large forces sit outside it, both of them real, and both of them working against the number on the screen.

• Tax on the interest, which is generally assessable income in the year it is earned, so the amount actually compounding is lower than the amount shown
• Inflation, which erodes what the final balance buys even while the balance grows
• Account fees, withdrawals and any change to the rate part way through, none of which the tool asks for
• Introductory or bonus rates that revert after a few months, which the tool has no way to represent

None of that means the exercise is pointless. It means the headline balance is a gross, before-tax, before-inflation figure, and you should read it as the shape of the growth rather than the money in your hand in twenty years.

One more limit, and it is ours. We hold an Australian Credit Licence and we advise on borrowing, so where to invest, what a product will return and how a balance should be structured for tax are questions for a licensed financial adviser, not for us.

What we can do is the debt side, properly. Every figure on this page is an estimate from the numbers you entered rather than an offer or an approval, and if the mortgage half is what caught your attention, we compare a panel of more than 40 lenders to see what your loan should actually be costing.