Free Compound Interest Calculator

What Is Compound Interest?

Compound interest is the process of earning interest on both your original principal and on previously accumulated interest. Unlike simple interest, which only applies to the initial amount, compound interest causes your savings or balance to grow geometrically when a constant positive rate is reinvested. The calculator models that assumption; it does not predict market returns.

For example, with $10,000 at a constant 6% nominal rate compounded annually and no deposits, you earn $600 in the first year. In the second year, you earn interest on $10,600 instead of just $10,000, yielding $636. The second-year ending balance is $11,236. Taxes, fees, withdrawals, and changing rates would change these results.

How to Use This Compound Interest Calculator

1. 1

   Enter Your Initial Principal

   Type the starting amount you plan to invest or save. This is the lump sum that will begin earning compound interest immediately.

2. 2

   Set the Interest Rate and Compounding

   Enter the nominal annual interest rate and choose how often interest compounds: annually, monthly, daily, or continuously. More frequent compounding yields slightly higher modeled balances at the same positive nominal rate.

3. 3

   Add Optional Contributions

   Specify any regular deposits you plan to make monthly or annually. Choose whether contributions are made at the beginning or end of each period.

4. 4

   Click Calculate and Review Results

   View your future value, total interest earned, a breakdown pie chart, growth bar chart, and a detailed year-by-year or month-by-month accumulation schedule.

Compound Interest Formulas

The basic formula for compound interest is:

Where:

• P — principal amount (initial investment)
• A — future value after time t
• r — annual interest rate (decimal)
• n — number of compounding periods per year
• t — number of years

For continuous compounding, the formula becomes:

Where e is Euler's number, approximately 2.71828. Continuous compounding represents the theoretical limiting growth rate as compounding frequency increases at a fixed positive nominal rate.

For the monthly schedule, the calculator uses an equivalent monthly factor: (1 + r/n)^n/12, or e^r/12 for continuous compounding. Each month it adds a beginning deposit, applies that factor, then adds any end deposit. This interpolates annual or quarterly growth across months; it does not simulate a bank's exact crediting dates. See the CFPB APY calculation rules for deposit disclosure conventions, and the SEC's scenario calculator for a separate educational tool.

Understanding Compounding Frequencies

The frequency specifies the nominal-rate conversion in this model. Actual accounts can use different day counts and crediting rules. This is not a mortgage or credit-card balance calculator. It supports nine frequencies: annually, semiannually, quarterly, monthly, semimonthly, biweekly, weekly, daily, and continuously.

For example, $10,000 at 6% for 10 years produces different results depending on compounding frequency: annually yields $17,908, monthly yields $18,194, daily yields $18,220, and continuously yields $18,221. While the differences may seem small, they compound significantly over longer time horizons and with larger principal amounts.

The Rule of 72

The Rule of 72 is a quick mental math shortcut to estimate how long it takes for money to double at a given interest rate. Simply divide 72 by the annual rate of return. At 6%, your money doubles in approximately 12 years. At 8%, it doubles in about 9 years. At 12%, it doubles in roughly 6 years. The exact doubling time under annual compounding is ln(2) / ln(1 + r), using r as a decimal. It is about 11.90 years at 6%; the shortcut does not model variable returns.

Why Use Our Compound Interest Calculator?