How Compound Interest Works
Compound interest means you earn interest on your principal and on the interest you've already earned. Each compounding period, your earned interest is added to the principal, and the next period's interest is calculated on the new, larger balance.
This "interest on interest" effect causes exponential rather than linear growth — the longer money is invested, the more powerful compounding becomes. Albert Einstein reportedly called compound interest the "eighth wonder of the world."
The Compound Interest Formula
The standard formula for compound interest is:
A = P(1 + r/n)^(nt)
- A — Final amount (principal + interest)
- P — Principal (initial investment)
- r — Annual interest rate (as a decimal, e.g. 0.07 for 7%)
- n — Number of times interest compounds per year
- t — Time in years
Example: $10,000 invested at 7% annual interest, compounded monthly for 10 years: A = 10,000 × (1 + 0.07/12)^(12 × 10) = $20,097
Compounding Frequency Matters
The more frequently interest compounds, the more you earn. For a $10,000 investment at 7% for 10 years, here's how the ending balance differs:
- Annually (n=1): ≈ $19,672
- Quarterly (n=4): ≈ $20,016
- Monthly (n=12): ≈ $20,097
- Daily (n=365): ≈ $20,137
The difference between monthly and daily compounding is small — but annual vs. monthly can be hundreds of dollars over a decade.
The Rule of 72
A quick mental math shortcut: divide 72 by your annual interest rate to estimate how many years it takes to double your money. At 6%, doubling takes about 72 ÷ 6 = 12 years. At 9%, it takes 72 ÷ 9 = 8 years. The Rule of 72 works best for rates between 6% and 10%.
Frequently Asked Questions
How often should interest compound for maximum growth?
More frequent compounding = more growth. Daily compounding earns slightly more than monthly, which earns more than annual. In practice, most savings accounts and investments compound daily or monthly. The difference between daily and monthly is small for most balances.
What is the Rule of 72?
Divide 72 by the annual interest rate to estimate how many years it takes to double your money. At 8% annually, your investment doubles in roughly 72 ÷ 8 = 9 years. At 6%, it takes about 12 years.
Does this include additional contributions?
This calculator handles a one-time principal investment. For ongoing monthly contributions, use the Savings Calculator, which supports regular deposits alongside compound interest.
What's a realistic interest rate to use?
High-yield savings accounts currently offer 4–5%. Money market accounts are similar. Bonds have historically returned 3–5%. Diversified stock market index funds have averaged 7–10% annually over the long term. Use realistic rates for your specific investment type.