Compound Interest Calculator

Calculate and compare compound interest across different compounding periods to maximize your investment growth. Explore the power of compound interest over time for financial planning.

Interest Rate Conversion

%

How to use:

  • • Enter your interest rate as a percentage
  • • Select how often the input rate compounds
  • • Choose the output compounding frequency
  • • The equivalent rate will be calculated automatically

Enter investment details to calculate compound interest.

Understanding Compound Interest

Interest is the cost of using borrowed money or the return earned on invested money. Understanding the difference between simple and compound interest is crucial for making informed financial decisions and maximizing your wealth-building potential.

Simple vs. Compound Interest

Simple Interest

Interest earned only on the principal (original amount). The interest stays constant each period. Formula: Principal × Rate × Time

Compound Interest

Interest earned on both principal AND accumulated interest from previous periods. This creates exponential growth over time.

Compound Interest Example

Real-World Example:

If you invest $1,000 at 10% interest for 2 years:

Simple Interest:

Year 1: $1,000 × 10% = $100 → Balance: $1,100

Year 2: $1,000 × 10% = $100 → Balance: $1,200

Compound Interest:

Year 1: $1,000 × 10% = $100 → Balance: $1,100

Year 2: $1,100 × 10% = $110 → Balance: $1,210

Compound interest advantage: $10 extra

Why Compound Interest Matters

  • Exponential Growth: The longer your money compounds, the faster it grows. This exponential effect becomes dramatic over decades
  • Time is Critical: Starting early gives your money more time to compound. Even small amounts invested young can outperform larger amounts invested later
  • Reinvestment Power: Automatically reinvesting dividends, interest, and gains maximizes the compounding effect
  • The Rule of 72: Divide 72 by your interest rate to estimate how long it takes to double your money. At 6%, money doubles in about 12 years

Compounding Frequencies & Their Impact

Interest can compound on different frequency schedules, and this significantly impacts your returns. Understanding how compounding frequency works helps you choose the best savings and investment options for maximum growth.

Common Compounding Frequencies

Annual Compounding

Interest is calculated and added once per year. Most common for CDs and some savings accounts. Provides the baseline for comparison with other frequencies.

Semi-Annual Compounding

Interest compounds twice per year (every 6 months). Often used for bonds and some investment products. Provides moderately better returns than annual.

Quarterly Compounding

Interest compounds four times per year (every 3 months). Common for many savings accounts and some CDs. Noticeable improvement over annual compounding.

Monthly Compounding

Interest compounds twelve times per year. Very common for savings accounts, mortgages, and credit cards. Significant improvement over annual compounding.

Daily Compounding

Interest compounds 365 times per year. Offered by many high-yield savings accounts and money market accounts. Provides near-maximum benefit.

Continuous Compounding

Mathematical limit where interest compounds infinitely often. Theoretical maximum return for any given interest rate. Used in advanced financial modeling.

Impact on Different Financial Products

  • Savings Accounts: Most compound daily or monthly. High-yield online savings accounts often compound daily for maximum growth
  • Certificates of Deposit (CDs): Usually compound monthly, quarterly, or annually. Longer-term CDs may have different compounding schedules
  • Credit Cards: Almost always compound daily, which works against you. This is why carrying a balance is so expensive
  • Mortgages & Loans: Typically compound monthly. This frequency affects your total interest paid over the life of the loan
  • Investment Accounts: Depends on the investment type. Dividend reinvestment creates effective compounding when earnings are reinvested

Frequency Comparison Example

Real Impact Example:

$10,000 at 6% interest for 10 years:

• Annual: $17,908.48

• Quarterly: $18,061.11

• Monthly: $18,193.97

• Daily: $18,220.07

Daily vs. Annual difference: $311.59

Compound Interest Formulas & Mathematics

Understanding the mathematical formulas behind compound interest helps you better grasp how your money grows and make more informed financial decisions. Our calculator handles the complex math, but knowing the formulas provides valuable insight.

Basic Compound Interest Formula

Standard Compound Interest:
At = A0(1 + r)n

Where:

  • • At = Final amount after time t
  • • A0 = Principal (initial investment)
  • • r = Annual interest rate (as decimal)
  • • n = Number of compounding periods (usually years)

Different Compounding Frequencies

Multiple Compounding Periods Per Year:
At = A0 × (1 + r/n)nt

Where:

  • • At = Final amount after time t
  • • A0 = Principal (initial investment)
  • • r = Annual interest rate (as decimal)
  • • n = Number of compounding periods per year
  • • t = Number of years

Examples:

  • • Monthly: n = 12
  • • Quarterly: n = 4
  • • Daily: n = 365

Continuous Compounding

Mathematical Limit of Compounding:
At = A0ert

Where:

  • • At = Final amount after time t
  • • A0 = Principal (initial investment)
  • • e = Mathematical constant (~2.718)
  • • r = Annual interest rate (as decimal)
  • • t = Number of years

Effective Annual Rate (APY)

  • APY Formula: APY = (1 + r/n)ⁿ - 1, where r is nominal rate and n is compounding frequency per year
  • Why APY Matters: APY accounts for compounding effects, giving you the true annual return for comparison shopping
  • APR vs APY: APR is the simple annual rate. APY includes compounding effects and is always higher than or equal to APR
Practical Application: While these formulas are mathematically precise, our calculator above handles all the complex computations for you. Use these formulas to understand the underlying principles and verify calculator results for your specific scenarios.

Frequently Asked Questions About Compound Interest