Compound Interest Calculator
How It Works
Compound interest is the process of earning interest on both your original principal and the interest you've already accumulated. Unlike simple interest — which only grows your initial deposit — compound interest allows your money to snowball over time, generating returns on your returns. Albert Einstein reportedly called compound interest the "eighth wonder of the world," and while the quote is likely apocryphal, the math behind it is very real.
The key to understanding compound interest is the compounding frequency: how often your interest is calculated and added to your balance. The more frequently your interest compounds, the faster your money grows. Daily compounding produces slightly more than monthly, which produces more than annual — because each period's interest starts earning interest sooner.
Time is the most powerful variable in compound interest. A dollar invested at age 25 has 40 years to compound before retirement; the same dollar invested at 45 has only 20. This difference compounds dramatically — the 25-year-old's dollar could be worth 4x as much at retirement, even with identical interest rates. This is why financial advisors consistently emphasize starting early, even with small amounts.
Regular contributions amplify the effect significantly. Adding $200 per month alongside a $10,000 initial investment at 7% over 30 years doesn't just add $72,000 in contributions — it adds over $240,000 in total value, because each contribution has time to compound. The chart below shows exactly how contributions and interest stack up year by year.
When comparing savings accounts, bonds, or investment accounts, the Annual Percentage Yield (APY) already accounts for compounding frequency — it's the effective annual rate after compounding. The nominal rate (APR) is always lower than APY when compounding happens more than once per year. This calculator uses the nominal rate to show you exactly how compounding works mathematically.
Formula Breakdown
The compound interest formula with regular contributions is: A = P(1 + r/n)^(nt) + PMT × [((1 + r/n)^(nt) - 1) / (r/n)] Where: - A = Final balance - P = Principal (initial investment) - r = Annual interest rate as a decimal (e.g., 7% = 0.07) - n = Number of times interest compounds per year (12 for monthly) - t = Time in years - PMT = Periodic contribution (monthly contribution converted to per-period) Example: $10,000 initial investment at 7% annual rate, compounding monthly, with $200/month for 30 years: - r/n = 0.07 / 12 = 0.005833 (monthly rate) - nt = 12 × 30 = 360 periods - Growth factor = (1.005833)^360 ≈ 8.116 - Principal portion: $10,000 × 8.116 ≈ $81,165 - Contribution portion: $200 × (8.116 - 1) / 0.005833 ≈ $242,975 - Final balance ≈ $324,140
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