Compound Interest Calculator
See how interest earns interest over time. Enter your principal, annual rate, compounding frequency, and time horizon to reveal the final amount, total interest earned, and effective annual rate.
How It Works
Compound interest is often called the eighth wonder of the world — and for good reason. Unlike simple interest, which is calculated only on the original principal, compound interest is calculated on the principal plus all previously accumulated interest. This means each compounding period adds interest to a larger base, creating exponential growth.
The formula is: A = P × (1 + r/n)^(n×t)
Where A is the final amount, P is the principal, r is the annual interest rate (as a decimal), n is the number of compounding periods per year, and t is the time in years.
Total interest earned = A − P
Effective Annual Rate (EAR) = (1 + r/n)^n − 1
The EAR is the rate that produces the same result as compounding. For example, 6% compounded monthly has an EAR of (1 + 0.06/12)^12 − 1 = 6.168%. This is useful when comparing accounts with different compounding frequencies.
Worked example: $10,000 invested at 7% per year, compounded monthly, for 20 years.
r = 0.07, n = 12, t = 20
A = 10000 × (1 + 0.07/12)^(12×20)
A = 10000 × (1.005833)^240
A = 10000 × 4.0387
A ≈ $40,387
Total interest = $40,387 − $10,000 = $30,387
The same $10,000 at simple interest would only return 10000 + (10000 × 0.07 × 20) = $24,000. Compounding adds an extra $16,387 — purely from interest earning interest.
Compounding frequency matters. Daily compounding of 7% gives $40,495 vs $40,387 for monthly — only $108 difference over 20 years. The rate and time are far more powerful variables than frequency.
The rule of 72: divide 72 by the annual interest rate to estimate how many years it takes to double. At 6%, money doubles in roughly 72/6 = 12 years. At 9%, it doubles in about 8 years.
Frequently Asked Questions
What is the difference between compound and simple interest?
Simple interest is calculated only on the original principal every period. Compound interest is calculated on the principal plus all accumulated interest, so each period's base is larger. Over time, compound interest grows much faster — the longer the period and higher the rate, the larger the gap.
Which compounding frequency is best for investors?
More frequent compounding gives a slightly higher return. However, the difference between daily and monthly compounding is very small. What matters far more is the stated annual rate and how long the money stays invested. Focus on rate and time first.
What is the effective annual rate?
The Effective Annual Rate (EAR) is the actual annual return after accounting for compounding. It is always equal to or higher than the nominal (stated) rate. Use it to compare savings accounts or bonds that compound at different frequencies — the account with the higher EAR will grow faster.
Does inflation affect compound interest?
Yes. If your investment earns 7% compound interest but inflation is 3%, your real return is approximately 3.9% (using the Fisher equation). To preserve purchasing power, your nominal return must exceed inflation. This calculator shows nominal growth; subtract inflation to get real growth.
How does this apply to debt?
Compound interest works against you on debt. Credit cards often compound daily. A $5,000 balance at 22% APR compounded daily grows to roughly $6,246 in one year if you make no payments. Paying off high-interest debt is mathematically equivalent to earning that interest rate, tax-free.