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.

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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