What is compound interest and how does it work?

What compound interest means

Compound interest is growth that occurs when the earnings on a balance are reinvested. Once those earnings become part of the principal, they can earn a return too. This is why compounding is often described as “interest on interest.”

For savings or investments, the principal is the amount you start with. Interest is the return generated during a period. Reinvestment means leaving that return in the account instead of withdrawing it.

The basic mathematics

For a fixed rate and no additional deposits, the idea can be written as:

ending balance = initial principal x (1 + rate) ^ periods

Suppose the principal is 100, the rate is 10% per period and the money remains invested for three periods:

ending balance = 100 x (1 + 0.10) ^ 3
ending balance = 100 x 1.331
ending balance = 133.10

This simplified formula assumes a constant rate and excludes contributions, fees and taxes. Real results can differ when any of those factors change.

A three-year example

Imagine investing $1,000 at 10% a year and reinvesting the interest annually:

The return increases from $100 to $110 and then $121, even though the rate stays at 10%. Each year begins with a larger balance.

Why time matters

Compounding often looks slow at first because earnings are being generated from a relatively small base. If returns remain invested, that base grows and each later period has the potential to produce more.

That does not make returns certain. Market values and rates can move, and fees, taxes and inflation can reduce the result. The lesson is narrower: principal and reinvested earnings have more opportunities to grow when they remain invested for longer.

The outcome depends mainly on the starting balance, rate, time horizon, compounding frequency and any recurring contributions. A higher expected rate can also involve greater risk; it should never be treated as a free increase in return.

For the variables and formulas in detail, see the compound interest formula. You can also compare simple and compound interest or use the Rule of 72 for a quick doubling-time estimate.

When compounding works against you

The same mechanism can apply to debt. If unpaid interest is added to a credit-card or loan balance, future interest may be calculated on that larger amount. Compounding is therefore neither inherently good nor bad: it can help when returns accumulate for you and hurt when charges accumulate against you.

Before borrowing, review the rate, fees, total cost and rules for missed payments. A low scheduled payment does not necessarily mean a low-cost debt.

Model your own scenario

Use the compound interest calculator to change the initial principal, rate, term, compounding frequency and contributions. It separates the amount contributed from the interest generated and shows how the balance changes over time.

Treat the result as an educational projection, not a forecast. A general calculator does not know future rates, market movements, taxes or product-specific fees.

Frequently asked questions

What does “interest on interest” mean?

It means that previously earned interest has been added to the principal and can itself generate interest in later periods.

Is compound interest always beneficial?

No. Reinvested returns may support long-term growth, but accumulated interest can also make debt more expensive.

What is needed for compounding to occur?

You need a balance, a return or interest rate, time and reinvestment. Regular contributions can increase the balance, but they do not guarantee a return.

Does the calculator include taxes and fees?

No. It is a mathematical estimate. Account for taxes, fees, penalties, variable rates and investment risk separately.

Sources

Banco de México’s financial education material explains simple and compound interest, while Condusef discusses reinvestment in the context of long-term saving.