Compound Interest Calculator

Compound Interest Formula Explained

The standard compound interest formula is A = P(1 + r/n)^nt, where:

• A = Final amount (future value)
• P = Principal (starting balance)
• r = Annual interest rate as a decimal (e.g. 6% = 0.06)
• n = Number of times interest compounds per year
• t = Time in years

Example: $5,000 at 6% annual interest, compounded monthly (n=12) for 10 years:
A = 5000 × (1 + 0.06/12)^12×10 = 5000 × (1.005)¹²⁰ = $9,096.98
That's $4,096.98 in interest earned on a $5,000 starting balance — without adding a single extra dollar.

For continuous compounding, use: A = Pe^rt, where e ≈ 2.71828. At continuous compounding, $5,000 at 6% for 10 years = $5,000 × e^0.6 = $9,110.59 — slightly more than monthly compounding.

Compound Interest vs Simple Interest

Simple interest is calculated only on the original principal: A = P(1 + rt). Compound interest earns "interest on interest," producing dramatically larger results over time. Here's how $10,000 at 5% compares:

After 30 years, compound interest produces $18,219 more than simple interest on the same $10,000 investment. The longer the time horizon, the more powerful compounding becomes. Use our Retirement Calculator to see how compound interest can grow your retirement savings over time.

How Compounding Frequency Affects Growth

More frequent compounding means slightly more interest earned each year. Here's how $10,000 at 6% grows over 10 years depending on compounding frequency:

The difference between annual and daily compounding is only $313 on a $10,000 investment over 10 years. However, on a $100,000 portfolio over 30 years, that gap widens significantly. The Effective Annual Rate (EAR) — also called the Annual Percentage Yield (APY) — captures this difference: at 6% compounded monthly, the EAR is 6.168%.

The Rule of 72

The Rule of 72 is a simple mental math shortcut for estimating how long it takes an investment to double. Divide 72 by the annual interest rate:

Years to Double ≈ 72 ÷ Annual Interest Rate

• At 6% — doubles in about 12 years (72 ÷ 6 = 12)
• At 8% — doubles in about 9 years (72 ÷ 8 = 9)
• At 10% — doubles in about 7.2 years (72 ÷ 10 = 7.2)
• At 12% — doubles in about 6 years (72 ÷ 12 = 6)

The Rule of 72 is a rough approximation — it's most accurate for rates between 6% and 10%. For more precise calculations, use our calculator above. Notably, the rule also works in reverse for debt: a credit card charging 18% APR will double your balance in just 4 years (72 ÷ 18 = 4) if you make no payments.

Real-World Compound Interest Examples

Here are three practical scenarios showing the power of compound interest in everyday financial life:

The $500/month scenario illustrates how consistent contributions dramatically amplify compound interest. Over 30 years you contribute $180,000 (500 × 360 months) but end up with $679,699 — meaning compound interest added $499,699, nearly 2.8× your total contributions. This is why financial advisors emphasize starting as early as possible.

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