Compound interest explained: how your money grows over time

Compound interest is the closest thing personal finance has to magic, and it's completely ordinary maths. It's the reason starting early beats starting big, and why long-term saving quietly does most of the work for you. Here's how it actually works, and what to watch for in a New Zealand context.

What is compound interest?

Simple interest pays you a return on your original amount only. Compound interest pays you a return on your original amount plus all the returns you've already earned. Each period the interest is added to your balance, and the next period's interest is worked out on that bigger balance.

That small difference snowballs. Early on it's barely noticeable. Given enough years, the interest earning interest becomes the biggest part of your balance, and your money grows faster and faster without you doing anything extra.

A quick example

Say you put in $10,000 at a 5% annual return and leave it untouched:

• After 1 year: $10,500
• After 10 years: about $16,289
• After 20 years: about $26,533
• After 30 years: about $43,219

You didn't add a cent after the first deposit. More than $33,000 of that final balance is interest, most of it earned in the later years as the snowball picks up speed. You can try your own numbers with the compound interest calculator.

The two things that supercharge it

Time. Because growth accelerates, the years at the end are worth far more than the years at the start. Someone who saves a modest amount from their twenties usually ends up ahead of someone who saves much more but starts in their forties. If there's one takeaway, it's that starting is worth more than optimising.

Regular contributions. Adding a bit every week or month, on top of a starting balance, dramatically changes the outcome. Each contribution gets its own runway to compound. Over a long enough period, it's normal for the total interest to end up larger than everything you actually put in. The year-by-year breakdown in the calculator shows the point where interest starts to overtake your own contributions.

How it applies in New Zealand

• Savings accounts and term deposits. The rate is known in advance. A term deposit locks a rate for a fixed term; banks may compound it on a set schedule (for example quarterly, or paid at maturity), so treat any calculator result as a close estimate rather than an exact quote. For a plain lump sum, set the regular top-up to $0.
• KiwiSaver and managed funds. Here the "rate" is an assumption, not a promise. Returns vary year to year and can be negative, but over decades the compounding effect on regular contributions is exactly what makes KiwiSaver powerful. See the KiwiSaver max-out calculator for the contributions side.

The catch: tax and fees

This is where being honest matters. Compound-interest calculators, including ours, usually show gross growth, before tax and fees. In New Zealand:

• Interest and investment income are generally taxed (RWT on bank interest, or PIE tax on KiwiSaver and PIE funds), which trims the effective rate.
• Managed funds and KiwiSaver charge fees, and even a small annual fee compounds against you over decades.

So your real balance will usually be somewhat lower than a gross projection. That doesn't undo the power of compounding, it just means you should treat the headline figure as the optimistic case, and try a slightly lower rate to see a more conservative outcome.

The short version

Compound interest is interest on your interest, and time is its most important ingredient. Start early, contribute regularly, and let it run. Model it with the compound interest calculator, remembering that real returns come after tax and fees, and aren't guaranteed.

This is general information, not financial advice. Investment returns vary and can be negative, so do your own research or talk to a licensed adviser before making decisions.