How Compound Interest Works

What compound interest is

Interest is the cost of borrowing money, or the reward for saving it. With simple interest, interest is calculated only on the original amount. With compound interest, interest is calculated on the original amount plus the interest already added. So you earn interest on your interest.

The basic formula

For a single deposit with no further additions:

Final amount = starting amount × (1 + rate)^{number of periods}

The rate is written as a decimal, so 10% is 0.10. A period is the length of time between interest additions, such as a year or a month.

A worked example

This example uses Nigerian naira (₦). The 10% yearly rate is made up for teaching and is not a prediction or an offer. Real rates vary by provider and over time. Interest here is added once a year, and no fees or taxes are included.

Start with ₦100,000 and add nothing more:

Simple interest adds the same ₦10,000 every year. Compound interest adds more each year, because each year's interest is calculated on a larger balance. For example, year 2 interest is 10% of ₦110,000, which is ₦11,000. The gap starts small and grows the longer money stays invested. The 10-year figure is rounded to the nearest naira.

Why time matters most

Compounding rewards patience. The longer money has to grow, the larger the effect. Starting earlier with a small amount can matter more than starting later with a bigger one. This is why saving a little regularly, from an early age, is so often recommended.

A rough shortcut is the rule of 72. Divide 72 by the yearly rate to estimate how many years it takes money to double. At 10%, that is 72 ÷ 10 = 7.2, so roughly 7 years. It is an approximation, not an exact result.

Compounding works against you on debt

The same effect applies to borrowing. If interest on a debt is added to the balance and you do not pay it down, the amount owed grows faster over time.

Illustration only: a debt of ₦100,000 with 2% interest added each month and no payments grows to about ₦126,824 after 12 months (₦100,000 × 1.02¹²). That is ₦26,824 of interest in a year. This is why paying down high-interest debt early matters, and why you should always check the real rate and terms before borrowing. Our guides on managing debt will cover this in more detail.

What affects how much you earn

• The rate: a higher rate grows money faster, but higher returns usually come with higher risk.
• How often interest is added: more frequent compounding gives slightly more.
• How long you leave it: time is the biggest factor.
• Regular additions: adding money over time increases the total further.
• Fees, taxes and inflation: these reduce what you actually keep and what it can buy.

Common mistakes

• Treating example rates as guaranteed returns.
• Ignoring fees, taxes and inflation.
• Waiting years to start because the amount seems too small.
• Withdrawing early and losing the compounding effect.
• Overlooking compounding interest on debt.

Frequently asked questions