How Compound Interest Works: Formula and Growth Examples

What compounding changes

With simple interest, interest is calculated only on the original principal in the basic model. With compound interest, retained interest becomes part of the balance that can earn more interest. This creates an accelerating dollar increase when a positive rate stays constant.

For example, $1,000 earning a fixed 5% annually becomes $1,050 after one year and $1,102.50 after two. The second year’s $52.50 includes $2.50 earned on the first year’s interest. Investor.gov’s calculator uses starting capital, contributions, time, and an assumed rate to explore this same relationship. ^[1]

The mechanism is mathematical. It does not mean an investment supplies a stable rate, avoids losses, or grows on a predictable schedule.

The basic formula

For starting principal P, nominal annual rate r, compounding periods per year n, and time in years t:

Future value = P × (1 + r ÷ n)ⁿᵗ

A $10,000 deposit at a fixed 5% nominal annual rate, compounded monthly for 10 years, grows to approximately $16,470.09 before taxes and fees. At 0%, it remains $10,000.

If you start with an APY rather than a nominal rate, use P × (1 + APY)ᵗ. Dividing an APY by 12 and treating the result as an exact monthly rate slightly changes the meaning. The monthly rate equivalent to an APY is (1 + APY)^(1/12) − 1.

Add monthly contributions consistently

For a monthly growth rate i, a constant end-of-month deposit C, and m months:

Future value = P × (1 + i)ᵐ + C × [(1 + i)ᵐ − 1] ÷ i

When i = 0, use P + C × m; the division formula would otherwise divide by zero. A beginning-of-month contribution earns one extra month of growth, so timing must be stated rather than silently mixed between examples.

For the worked example, deposits occur at the end of each month. Convert a nominal compounding frequency to an equivalent monthly growth rate when combining it with monthly deposits. Continuous compounding uses exp(r ÷ 12) − 1 as that monthly rate. This keeps the lump sum and recurring deposits on one consistent schedule.

Worked example: saving matters as much as the headline rate

Start with $10,000 and add $500 at the end of each month for 25 years. At an assumed 8% nominal rate compounded monthly, the projected ending balance is approximately $548,915. You contributed $160,000; the remaining roughly $388,991 is modeled growth.

That is not an expected or guaranteed market outcome. Repeat the calculation with a lower return, a shorter horizon, and interrupted contributions. A projection that works only with one optimistic rate is not a resilient plan.

Look at the contribution total beside the ending balance. During early years, increasing savings may change the result more than seeking a small return advantage. Later, a larger accumulated balance makes the assumed return much more influential.

Account for fees, taxes, and inflation

Investment expenses reduce the amount retained for future growth. Taxes may be due annually, at withdrawal, or under other rules depending on the account and investment. A tax-deferred balance is not automatically equal to spendable after-tax wealth.

Inflation changes what the future balance can buy. At 3% average inflation, a dollar 25 years from now has less purchasing power than a dollar today. For a constant-rate illustration, divide the future nominal balance by (1 + inflation rate)^years to express it in today’s dollars.

Do not subtract a fee twice when the assumed return already reflects it. Record whether the input is before or after fees and taxes.

Common mistakes to avoid

An arithmetic average return is not the same as compound annual growth. A 20% gain followed by a 20% loss takes $100 to $120 and then to $96, not back to $100. The order of returns also matters when contributions or withdrawals occur.

The “Rule of 72” is a rough estimate of doubling time for some positive rates, not an exact formula. A changing market, a changing savings rate, or a withdrawal plan needs a richer model than constant compounding.

Use compounding to understand relationships. Use a range of assumptions to make decisions.

Use this guide thoughtfully. Educational information, not individualized financial, investment, tax, or legal advice. Examples are hypothetical unless a source is explicitly identified. Verify current terms and consider qualified professional guidance for your situation.