What compound interest is
With compound interest, interest is added to the balance and then earns interest itself. Over long periods this produces growth that accelerates, unlike simple interest, which is calculated on the original amount only. This calculator projects a balance from a starting amount, a fixed annual rate, a compounding frequency and optional regular deposits.
Formulas
Lump sum: A = P × (1 + r/m)^(m × t)
Regular contributions (end of period): FV = C × ((1 + i)^(p × t) − 1) ÷ i, with i = (1 + r/m)^(m/p) − 1
- P = initial amount; C = contribution per period
- r = annual rate as a decimal; t = years
- m = compounding periods per year; p = contributions per year
- i = equivalent rate per contribution period, which handles contributions and compounding at different frequencies
Contributions made at the start of each period earn one extra period of interest, so their future value is multiplied by (1 + i). The calculator applies these steps period by period, which also produces the yearly table.
Worked examples
$10,000 at 5%, compounded monthly, for 10 years
- r/m = 0.05 ÷ 12 ≈ 0.0041667; m × t = 120.
- A = 10,000 × 1.0041667^120 ≈ $16,470.09; interest earned ≈ $6,470.09.
$100 a month at 5%, monthly compounding, 10 years
- i = 0.05 ÷ 12 (frequencies match); 120 deposits.
- FV = 100 × (1.0041667^120 − 1) ÷ 0.0041667 ≈ $15,528.23 from $12,000 contributed.
$5,000 at 6%, compounded annually, 20 years
A = 5,000 × 1.06^20 ≈ $16,035.68.
Interpreting results
"Interest earned" is the balance minus everything you put in. The year-by-year table shows that interest grows faster in later years. Inflation, taxes and fees are not included, so the balance is a nominal figure, not purchasing power.
Common mistakes
- Entering an APY as if it were a nominal rate with monthly compounding, which slightly overstates growth. If a bank quotes APY, choose annual compounding.
- Expecting a fixed rate from investments. Market returns vary and can be negative.
- Ignoring contribution timing; start-of-period deposits grow slightly more.
Assumptions and limitations
One constant rate, no withdrawals, taxes or fees, whole years, and contributions of the same size throughout. This is an educational projection, not investment advice. The U.S. Securities and Exchange Commission's Investor.gov site has further material on compounding.
Related: loan payment calculator, mortgage calculator, percentage calculator.
Frequently asked questions
Does more frequent compounding make a big difference?
Less than most people expect at ordinary rates. $10,000 at 5% for 10 years grows to $16,288.95 with annual compounding and $16,470.09 with monthly compounding, a difference of about 1.1%.
What is the rule of 72?
A quick estimate: divide 72 by the annual percentage rate to approximate the years needed to double. At 6%, about 12 years; the exact figure with annual compounding is 11.9 years.
Are these returns guaranteed?
No. The calculator applies one fixed rate every period. Savings account rates change, and investment returns vary from year to year and can be negative.