Compound interest is interest calculated on both your original amount and the interest already added, so the balance grows a little faster each period. The effect is small at first and larger over long periods, which is why time matters so much.
The same principle works in reverse on borrowed money, which is why it is worth understanding either way.
Simple versus compound interest
With simple interest, you earn only on the original amount, called the principal. If you put 1,000 into an account paying 5 per cent simple interest, you earn 50 each year, every year.
With compound interest, each year’s interest is added to the balance, and the next year’s interest is calculated on the larger total. The interest itself starts earning interest.
A worked example of compound interest
Suppose you deposit 1,000 and it earns 5 per cent a year, compounded annually, with no further deposits. The 5 per cent rate is purely for illustration; real rates vary and are never guaranteed.
| Year | Start balance | Interest at 5% | End balance |
|---|---|---|---|
| 1 | 1,000.00 | 50.00 | 1,050.00 |
| 2 | 1,050.00 | 52.50 | 1,102.50 |
| 3 | 1,102.50 | 55.13 | 1,157.63 |
| 4 | 1,157.63 | 57.88 | 1,215.51 |
| 5 | 1,215.51 | 60.78 | 1,276.28 |
After five years, simple interest would give 1,250, while compounding gives about 1,276. The gap of roughly 26 looks modest, but it widens each year. Over ten years the same example reaches about 1,629, compared with 1,500 under simple interest.
The formula in plain words
The balance after a number of years equals the starting amount multiplied by one plus the rate, raised to the power of the number of years. For our example: 1,000 x 1.05 x 1.05 x 1.05 and so on. You can check any row of the table with a calculator.
How often interest compounds
Interest may be added annually, monthly or even daily. More frequent compounding gives a slightly higher result at the same stated rate. The difference is usually small, but it explains why two accounts with the same headline rate can differ a little.
The Rule of 72
A well-known shortcut estimates how long it takes for money to double: divide 72 by the annual percentage rate. At 6 per cent, 72 divided by 6 is 12, so doubling takes around 12 years. At 3 per cent it is about 24 years. The rule is an approximation, but it is handy for mental estimates and it also reminds you how strongly the rate and time matter.
Why starting early helps
Because growth builds on past growth, time is the most powerful ingredient. Consider two savers using the same illustrative rate: one begins early with small amounts and the other begins later with bigger amounts. The early saver often has more time for compounding to work, even if total contributions are lower. Nothing here guarantees any outcome, since real-world returns vary, but the principle of time helping the balance is well established.
When compounding works against you
Debts such as credit cards often compound too. An unpaid balance that accrues interest on interest can grow faster than expected if only small payments are made. This is one reason many people prioritise repaying high-rate debts; compare approaches in debt snowball vs avalanche.
It also shows why paying more than the minimum matters. Each extra payment reduces the balance on which future interest is charged.
Putting it into practice
You do not need complicated tools. Use a savings calculator or a spreadsheet to test your own numbers, and focus on the things you control: how much you save, how regularly and for how long. A saving for a goal plan turns that into a monthly figure, while emergency fund basics covers the cushion to build first. Compare rates and fees carefully for any account, and see the finance archive for more basics.
This article is general educational information, not financial, tax or legal advice; please consult a qualified professional about your own situation.
Key takeaways
- Compound interest earns interest on previous interest, so balances grow faster over time.
- In our example, 1,000 at 5 per cent becomes about 1,276 after five years.
- The Rule of 72 gives a quick estimate of doubling time.
- Compounding also applies to debt, so repaying early matters.
Frequently asked questions
What is the difference between APR and APY?
APR is the yearly rate without compounding within the year, while APY includes the effect of compounding. APY is therefore usually slightly higher than APR for the same account.
Does compound interest guarantee growth?
No. The principle describes how interest accumulates when a rate is paid, but actual rates change and investments can lose value. Any example is only an illustration.
How do I calculate it myself?
Multiply your balance by one plus the rate for each period. A spreadsheet or online calculator can do this for any number of years.
Is compound interest good or bad?
It is neutral. It helps when you are earning interest on savings and hurts when you owe interest on debt.
Photo: Seedlings 2020 2 by City of Austin, Public domain, via Wikimedia Commons
