What is compound interest? A simple guide with examples

What is compound interest?

Compound interest is interest earned on the principal and also on the interest already accrued. Each period, the interest you earn is added to the balance, and in the next period it earns interest too. It is "interest on interest"¹.

The practical consequence: the base the interest is calculated on grows by itself, and the balance increases faster and faster.

Simple vs compound interest

With simple interest, interest is always calculated on the initial capital. The base never changes. With compound interest, the base includes the interest already credited, so each period earns a little more than the last.

Over short horizons the difference is small. Over long horizons it becomes huge, which is why compound interest matters so much for long-term saving and investing.

How is it calculated?

With monthly compounding and regular contributions, the future value is:

FV = P·(1+i)^n + PMT·((1+i)^n − 1) / i

where P is the initial capital, PMT the monthly contribution, i the annual rate divided by 12 and n the number of months. You don't need to do the maths by hand: use our compound interest calculator and see the result year by year.

Why does time matter so much?

Because each compounding cycle earns on a larger balance. With €1,000 to start and €100 per month at 5% a year, after 10 years you invest €13,000 and end with about €17,175. Over €4,000 comes from interest alone. The earlier you start, the more cycles happen.

The effect is not linear, it is exponential: in the early years the gap versus simple interest looks small, but it accelerates. On the same €1,000 at 5%, simple interest earns a flat €50 a year; with compounding, year 10's interest is calculated on a balance far larger than year 1's. That's why delaying the start is so costly: you don't just lose one year of contributions, you lose one of the most valuable cycles, the last one.

The rule of 72: how long money takes to double

There is a simple mental shortcut to estimate, without doing the maths, how long an investment takes to double with compound interest: the rule of 72. Divide 72 by the annual rate (as a percentage) and you get the approximate number of years. At 6% a year, capital doubles in about 72 ÷ 6 = 12 years; at 4%, in about 18 years; at 8%, in just 9. It is an approximation, not an exact calculation. It shows intuitively how higher rates and longer horizons reinforce each other.

The same rule works in reverse and helps you grasp the opposite risk: applied to inflation, it tells you how long prices take to double and the purchasing power of idle money halves. At 3% inflation, that happens in about 24 years: the same compounding engine, now working against you.

Annual, monthly or daily: compounding frequency

How often interest is credited also matters. The more frequent the compounding, the sooner the interest itself starts earning:

• Annual: interest credited once a year.
• Monthly: credited 12 times a year (the most common in savings accounts and tools).
• Daily: credited every day, the practical limit of the effect.

The gap between annual and monthly exists, but it is modest compared with the impact of time and the rate. Our calculator uses monthly compounding, a realistic starting point.

Nominal rate and effective rate (APY)

When interest compounds more than once a year, there are two rates to tell apart. The nominal rate is the one that gets advertised. The effective annual rate (often shown as APY) captures how much money actually earns over a year, once compounding is taken into account, and it is always slightly higher than the nominal rate when compounding is sub-annual (monthly, quarterly or daily).

An example: 6% nominal with monthly compounding works out to about 6.17% effective, because each month's interest already earns in the following months. The gap is small at low rates but grows with the rate and the frequency. So when comparing two products with different compounding frequencies, look at the effective rate, not the nominal one, only then is the comparison fair.

The role of regular contributions

The starting capital is only the beginning. Steady monthly contributions add to the balance and then earn interest themselves. Two people with the same rate and horizon can end with very different amounts depending on how much they add each month. In practice, consistency usually matters more than trying to time the "right" moment.

Compound interest and inflation

One important caveat: inflation erodes the purchasing power of money over time. A nominal balance growing 5% a year, with 2% inflation, grows about 3% in real terms. Compound interest is still a powerful force, but it's worth thinking about results in real terms, not just the nominal number.

Compound interest and taxes

There is a third factor, besides time and the rate, that changes the real result: taxes. In Portugal, capital income, interest included, is generally taxed at a flat 28% withholding rate, deducted at source². In practice, what compounds year after year is not the gross interest but the interest net of tax.

The effect is compounding in reverse: a 5% gross rate is worth about 3.6% net, and it is on that smaller figure that future interest is earned. So when projecting how a long-term saving will grow, it is worth thinking in net terms, and, ideally, in real terms too, after inflation. You can see the concrete impact of the tax in the term deposit simulator.

When compound interest works against you

The same mechanism that grows your savings can work against you when you have debt. On a credit card or an overdraft, the interest you don't pay is added to the outstanding balance and then earns interest itself. It is compounding, only in the lender's favour. That is why high-rate card debt grows so fast when it isn't paid off in full each month: next month's balance already includes this month's interest.

The lesson is symmetrical, and worth keeping. With investments, let time compound in your favour, start early and stay consistent. With expensive debt, do exactly the opposite: pay it down early to stop the compounding before it accelerates. Understanding compound interest is, ultimately, understanding the two faces of the same force.

Common mistakes to avoid

• Confusing simple and compound interest and underestimating long-term growth.
• Delaying the start to contribute more later, lost time is rarely recovered.
• Ignoring inflation and taxes on returns, which reduce the real value.
• Assuming a fixed, guaranteed rate, investments carry risk; the calculator is an estimate, not a promise.

How to start

You don't need to do the maths by hand. Set a starting amount, a realistic monthly contribution and a prudent rate, and see the result year by year. The goal isn't to predict the future to the cent, but to understand the order of magnitude and how time works in your favour.

Try your own figures in the compound interest calculator, or compare with simple interest to see the difference compounding makes.