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Interest on Interest

Compound Interest Calculator

See how a starting balance grows when interest earns interest — with optional monthly contributions and daily, monthly, quarterly, or annual compounding.

100% FreeYear-by-Year GrowthAny Compounding Frequency
Growth Inputs
Works for savings accounts, CDs, index funds — anything with a steady growth rate

Why Compound Interest Snowballs (Worked Example)

Simple interest pays only on the principal; compound interest pays on the principal plus every prior interest payment. $10,000 at 5% simple earns $500/year forever — $15,000 after 10 years. Compounded monthly, the same money reaches $16,470, and the gap accelerates: after 30 years it's $25,000 simple versus $44,677 compound. The curve is exponential — the last decade of a long horizon earns more than the first two combined.

Doubling Time by Rate (Rule of 72 vs Exact)

Annual rateExact doublingRule of 72
2%35.0 yr36 yr
4%17.7 yr18 yr
6%11.9 yr12 yr
8%9.0 yr9 yr
10%7.3 yr7.2 yr
12%6.1 yr6 yr

Exact doubling time is ln 2 ÷ ln(1 + r) with annual compounding.

Where Compounding Shows Up in Real Life

  • High-yield savings and CDs — daily compounding at the quoted APY; the growth table mirrors your statements.
  • Retirement investing — market returns aren't fixed, but long-run averages compound the same way; see our Dave Ramsey Investment and 401(k) calculators for retirement-flavored projections.
  • Debt, in reverse — credit-card balances compound against you daily at 20%+ APR, which is why minimum payments barely move the balance (our Amortization Calculator shows the payoff math).

Frequently Asked Questions

What is the compound interest formula?
A = P(1 + r/n)^(nt), where P is the principal, r the annual rate as a decimal, n the number of compounding periods per year, and t the years. $10,000 at 5% compounded monthly for 10 years: A = 10,000 × (1 + 0.05/12)^120 ≈ $16,470.
How much difference does compounding frequency make?
Less than most people expect. $10,000 at 5% for 10 years grows to $16,289 compounded annually, $16,470 monthly, and $16,486 daily — the jump from annual to monthly matters more than monthly to daily. The rate itself dwarfs the frequency.
What is the Rule of 72?
Divide 72 by the annual rate to estimate the years to double: at 6%, money doubles in about 12 years; at 9%, about 8 years. It's a mental shortcut derived from the exact doubling time ln(2)/ln(1+r), accurate within a few months for rates between 4% and 12%.
How do monthly contributions change the math?
Each deposit starts its own compounding clock. $100/month at 5% (monthly compounding) for 10 years contributes $12,000 but grows to about $15,528 — so with a $10,000 starting balance the total is roughly $32,000, of which about $10,000 is interest.
Is APR the same as APY?
No. APR is the quoted nominal rate; APY includes the effect of compounding. A 5% APR compounded monthly is an APY of (1 + 0.05/12)^12 − 1 = 5.12%. Banks advertise savings in APY and loans in APR — enter the APY here for deposit accounts.
Does this account for taxes or inflation?
No — results are nominal, pre-tax. Interest in taxable accounts is taxed yearly, which slows compounding; at 3% inflation, purchasing power halves roughly every 24 years (Rule of 72 again). For a real-terms estimate, subtract expected inflation from your rate.
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Disclaimer: This calculator is for general educational purposes only and is not financial, investment, tax, or legal advice. Results are estimates; consult a qualified professional before making financial decisions.