Understanding Compound Interest
Compound interest is interest calculated on both your original investment and the accumulated interest from previous periods — often described as "interest earning interest." This is fundamentally different from simple interest, which only ever calculates interest on the original principal amount. Over long time horizons, this difference becomes dramatic.
Albert Einstein reportedly called compound interest "the eighth wonder of the world" — while the quote's origin is disputed, the underlying math is real: the earlier you start investing, the more time compounding has to work, which often matters more than the amount you invest.
The Compound Interest Formula
A = P(1 + r/n)^(nt)
A = final amount
P = principal (starting amount)
r = annual interest rate (decimal)
n = compounding frequency per year
t = number of years
When regular monthly contributions are added (as this calculator does), the formula extends to include the future value of an annuity component on top of the base compounding.
Worked Example
Example
Starting with $10,000 and contributing $200/month at 8% annual return, compounded monthly, your balance grows to approximately $128,700 after 20 years — of which only $58,000 came from your own contributions. The remaining ~$70,700 came purely from compound growth.
Why Starting Early Matters
- Time matters more than amount — $200/month starting at age 25 typically outgrows $400/month starting at age 35, due to the extra decade of compounding.
- Compounding frequency matters less than you'd think — the difference between monthly and daily compounding is small; consistency of contributions matters far more.
- Higher returns come with higher risk — the 7-10% range modeled here typically reflects diversified stock market index investing, which carries more volatility than savings accounts (1-5%).
- Avoid early withdrawals — pulling money out resets the compounding clock on that portion, losing years of potential growth.
Frequently Asked Questions
What's a realistic annual return to use? ▼
For a diversified stock market index fund over long periods, 7-10% annually (before inflation) is a commonly cited historical average, though past performance doesn't guarantee future results. For more conservative savings accounts or CDs, 1-5% is more realistic depending on current rates.
How often should interest compound for the best results? ▼
More frequent compounding (daily vs monthly vs annually) does produce slightly higher returns, but the difference is small in practice — a few tenths of a percent over many years. Contributing consistently and starting early has far more impact than optimizing compounding frequency.
Does this calculator account for inflation or taxes? ▼
No — this calculator shows nominal (pre-tax, pre-inflation) growth. To estimate real purchasing power, subtract an assumed inflation rate (historically around 2-3% annually) from your return rate. Tax treatment varies by account type (401k, IRA, taxable brokerage) and isn't factored in here.
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