How Compound Interest Works (With Examples)

The formula

A = P × (1 + r ÷ n)^{n × t}

• A — final amount
• P — starting amount (principal)
• r — annual interest rate as a decimal (10% = 0.10)
• n — times interest is compounded per year
• t — number of years

Worked examples

Yearly compounding: 100,000 at 10% for 10 years: 100,000 × 1.10¹⁰ = 259,374.25. Simple interest would give only 200,000 — the extra 59,374 is interest earned on interest.

Monthly compounding: 50,000 at 12% a year, compounded monthly, for 10 years: 50,000 × (1 + 0.01)¹²⁰ ≈ 165,019.

With monthly deposits: the same 50,000 plus 5,000 at the end of every month comes to about 1,315,213 after 10 years. You paid in 650,000; roughly 665,000 is interest.

What changes the result most

• Time. Each extra year adds more than the one before. Starting early matters more than any other setting.
• Rate. Small differences add up: over 20 years, 12% grows money far more than 10%.
• Regular deposits. For most people, steady contributions do more than the starting amount.
• Compounding frequency. Monthly versus yearly makes a modest difference; it matters less than the rate and time.

Calculate your own

1. In the Compound Interest Calculator, enter the starting amount (it can be zero).
2. Enter the annual rate and the number of years.
3. Choose the compounding frequency your bank or provider states.
4. Add a regular deposit, monthly or yearly, at the start or end of each period.
5. Review the final balance, the interest earned and the year-by-year table, which you can download as CSV.

The rule of 72 and real-world limits

To estimate how long money takes to double, divide 72 by the annual rate: at 8%, about 9 years; at 12%, about 6 years.

The calculator assumes a constant rate. Real savings rates change, investment returns vary and can be negative, and taxes, fees and inflation reduce what you end up with. Treat the result as an illustration for planning, not financial advice; for decisions about your money, consult a qualified adviser.

Frequently asked questions