How Compound Interest Works (and the Formula)

How compound interest works

The core idea is growth on growth: earnings are folded back in.

• Each period, interest is added to the principal.
• The next period's interest is calculated on the larger balance.
• This repeats, so the base grows every period.
• The growth curve steepens over time rather than staying flat.

The compound interest formula explained

Each symbol maps to a real input.

• Future value = P times (1 + r/n) raised to (n times t).
• P is the principal, the amount you start with.
• r is the annual rate as a decimal and t is the years.
• n is how many times interest compounds per year.

Why compounding frequency matters

More frequent compounding earns slightly more.

• Yearly compounding adds interest once per year.
• Monthly compounding adds it twelve times, on a growing base each time.
• The more often it compounds, the higher the ending balance.
• The gain from frequency shrinks as it approaches continuous compounding.

Compound vs simple interest

The difference widens with time.

• Simple interest is calculated only on the original principal.
• $1,000 at 5 percent simple for 10 years earns a flat $500.
• The same amount compounded yearly grows to about $1,629.
• The extra $129 is interest that itself earned interest.

When compounding works against you

The same mechanism that grows savings also grows debt, so understanding it protects you from balances that quietly spiral.

• Unpaid credit-card interest compounds, often monthly, on a rising balance.
• A small carried balance can grow faster than intuition suggests over a year.
• Paying more than the minimum attacks the principal that future interest feeds on.
• The higher the rate, the more punishing the compounding becomes on debt.
• Treat high-interest debt as compounding in reverse and clear it before it snowballs.

Debt compounds too, and the Credit Card Payoff Calculator shows how a balance behaves over time when you only pay part of it.

A step-by-step growth example

Suppose you deposit $5,000 at 6 percent a year, compounded monthly, and leave it for 20 years. The monthly rate is 0.5 percent over 240 periods, so the balance grows to about $16,551. Simple interest at the same rate would only reach $11,000, which shows how much of the final sum is growth built on earlier growth.

• Add $100 each month and the same 20 years ends near $62,000, with only $29,000 of that contributed by you.
• Waiting ten years to start roughly halves the outcome, even if you deposit the same amount afterward.
• Raising the rate by one percentage point matters more the longer the money stays invested.

To model your own deposits and goals without doing the exponent by hand, the savings goal calculator guide walks through the inputs and how to read the chart.

Common compounding mistakes to avoid

Most wrong answers come from a small slip in setup rather than the maths itself. Watch for these when you check a result.

• Mixing units, for example using the annual rate with monthly periods, which understates or overstates growth by a wide margin.
• Forgetting that the quoted rate is nominal; the effective annual yield is slightly higher when compounding is frequent.
• Ignoring fees and inflation, which reduce the real return you actually keep.
• Assuming a return is guaranteed when savings rates and market returns change over time.

A quick sanity check helps: the rule of 72 says money doubles in roughly 72 divided by the percentage rate years, so 6 percent doubles in about 12 years. If your result disagrees wildly, revisit the inputs.

Step-by-step

Common mistakes to avoid

Pro tips

Frequently asked questions