The compound interest formula
Compound interest is interest you earn on both your original money and on the interest already added. The formula is A = P(1 + r ÷ n)n·t, where P is the principal, r is the annual rate as a decimal, n is how many times interest compounds per year, and t is the number of years. The interest earned is simply A − P. Unlike simple interest, which is paid only on the principal, compounding lets your balance accelerate over time because each period earns on a larger base.
How to use this calculator
Enter your principal (the starting deposit), the annual interest rate, the number of years you will leave it invested, and the compounds per year (12 for monthly, 4 for quarterly, 365 for daily, 1 for annual). The tool returns your future balance, the interest earned, and your original principal so you can see the split at a glance. To project a balance with no compounding detail, try the simpler future value calculator. Banks quote the compounded rate as APY, which the APY calculator converts for you.
Worked example and why frequency matters
Suppose you deposit $1,000 at a 5% annual rate compounded monthly for 10 years. Plugging in: A = 1000 × (1 + 0.05 ÷ 12)12 × 10 ≈ $1,647.01, so you earn about $647.01 in interest. The more often interest compounds, the more you earn for the same nominal rate:
| Compounding | n | Balance after 10 yrs |
|---|---|---|
| Annually | 1 | $1,628.89 |
| Quarterly | 4 | $1,643.62 |
| Monthly | 12 | $1,647.01 |
| Daily | 365 | $1,648.66 |
These figures are an estimate for general information only and are not financial advice; consult a qualified professional before making money decisions. If you plan to add money every month, the savings calculator handles the deposits too.
Frequently asked questions
- What is compound interest?
- Compound interest is interest calculated on both your original principal and the interest already accumulated. Over time this creates faster growth than simple interest, which is paid only on the principal.
- How much does $1,000 grow at 5% over 10 years?
- Compounded monthly at 5%, $1,000 grows to about $1,647.01 after 10 years, earning roughly $647.01 in interest.
- Does compounding more often earn more?
- Yes, but with diminishing returns. Moving from annual to monthly compounding adds noticeably more interest; moving from monthly to daily adds only a little extra.
- Is the interest shown here taxable?
- Interest from most accounts is taxable income. This calculator shows pre-tax growth and ignores fees, deposits after the start, and rate changes.
- What if I withdraw money before the term ends?
- The final balance falls by more than the amount you take out, because that money stops compounding for the remaining years. This calculator assumes the principal stays untouched for the full term with no deposits or withdrawals.