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Money & Finance

Compound Interest Explained With Examples

Learn how compound interest grows money faster than simple interest, with the formula, a worked example, and how compounding frequency changes the result.

Understanding the Calculation

Simple interest pays a fixed amount each period based only on the starting principal. Compound interest pays interest on the principal plus whatever interest has already accumulated, so the base the interest is calculated on grows every period.

The gap between simple and compound interest is small over short periods but becomes large over long ones, because compounding is exponential rather than linear. This is why long-term savings and retirement accounts benefit heavily from starting early.

How often interest compounds (annually, monthly, daily) also matters. More frequent compounding means interest starts earning its own interest sooner, which produces a slightly higher balance for the same nominal annual rate.

The Formula

Compound Interest Formula
A = P * (1 + r/n)^(n*t)

Each compounding period, the balance is multiplied by (1 + r/n). Doing that n*t times, once per period across the full term, is the same as raising (1 + r/n) to the power n*t.

Variables & Definitions

A— Future Value
The total balance after interest, including principal.
P— Principal
The original amount deposited or borrowed, before any interest.
r— Annual Interest Rate
The nominal yearly interest rate, expressed as a decimal (6% = 0.06).
n— Compounding Frequency
Number of times interest is compounded per year (12 for monthly, 365 for daily).
t— Time
The number of years the money grows for.

Worked Example

Worked Example: $10,000 at 6% Compounded Monthly for 10 Years

A $10,000 deposit earns a 6% annual interest rate, compounded monthly, left untouched for 10 years.

Starting Inputs
  • Principal:$10,000
  • Annual Rate:6%
  • Compounding Frequency:Monthly (n = 12)
  • Time:10 years
Step-by-Step Calculation
  1. 1

    Find the periodic rate

    Divide the annual rate by the number of compounding periods per year: 0.06 / 12 = 0.005.

    r/n = 0.06 / 12 = 0.005
    Result: 0.5% per month
  2. 2

    Find the total number of periods

    Multiply the number of years by the compounding frequency: 10 years * 12 months/year = 120 periods.

    n*t = 12 * 10 = 120
    Result: 120 monthly periods
  3. 3

    Apply the compound interest formula

    Raise (1 + 0.005) to the 120th power, then multiply by the principal.

    A = 10000 * (1.005)^120
    Result: A ≈ $18,193.97
  4. 4

    Compare with simple interest at the same rate

    Simple interest only ever applies to the original $10,000: A = P(1 + rt) = 10000 * (1 + 0.06 * 10) = $16,000.

    10000 * (1 + 0.6) = $16,000
    Result: $16,000 (simple interest)
Conclusion: Over 10 years, compounding monthly instead of using simple interest adds about $2,193.97 to the final balance, purely from interest earning interest on itself.

Calculate Your Own Numbers

Put these formulas into practice with our free, in-browser calculators:

Compound Interest Calculator

Project future value with custom principal, rate, compounding frequency, and periodic contributions.

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Savings Calculator

Model a savings account balance over time with regular deposits.

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Investment Calculator

Estimate investment growth under different rates of return and contribution schedules.

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What the Results Mean For You

  • The longer the time horizon, the bigger the gap between compound and simple interest becomes. Over 1 year, the difference is tiny; over 30 years, it can be the majority of the account's growth.
  • Compounding frequency matters less than most people expect once you're past a few compounds per year. Moving from monthly to daily compounding at the same annual rate produces only a small additional gain, since the periodic rate is already small.
  • Regular contributions on top of a lump sum change the math: each new deposit compounds for a shorter time than the original principal, so later contributions add less growth than earlier ones.

Common Pitfalls & Mistakes

Using the annual rate directly as the periodic rate

When compounding monthly, the rate used inside the formula for each period must be the annual rate divided by 12, not the annual rate itself.

Mixing up n*t with a single multiplication of years and rate

The exponent is the total number of compounding periods (frequency times years), not just the number of years — using years alone understates the growth for anything compounding more often than annually.

Assuming compounding frequency alone explains most of the growth

The overwhelming driver of long-term growth is time and rate, not how many times per year interest compounds. Doubling the compounding frequency does not come close to doubling the balance.

Authoritative References & Sources

All formula representations and regulatory context are verified against authoritative public sources:

  • Compound InterestU.S. Securities and Exchange Commission — Investor.gov

    Federal investor-education reference explaining the compound interest formula and its variables.

    Visit source documentation