Compound Interest Calculator

Visualize the Power of Compounding

Witness the power of compound interest—often called the eighth wonder of the world. This calculator projects the future value of your investment by considering your initial principal, regular contributions, annual interest rate, and how often the interest is compounded. It's a fundamental tool for retirement planning and achieving long-term savings goals.

The Compound Interest Formulas Explained

The calculator uses two main formulas:

1. Future Value of a Lump Sum: A = P(1 + r/n)^(nt)
   • This calculates the growth of your Initial Principal (P).
2. Future Value of a Series (Annuity): A = M * [((1 + i)^k - 1) / i]
   • This calculates the growth of your Monthly Contributions (M).

• r: Annual interest rate
• n: Number of times interest is compounded per year
• t: Number of years
• i: Interest rate per period (r/n)
• k: Total number of periods (nt)

The final result is the sum of both calculations.

How to Use the Calculator

1. Initial Principal: Enter your starting investment amount.
2. Annual Interest Rate: Input your expected annual rate of return.
3. Years to Grow: Enter the number of years you plan to invest.
4. Compound Frequency: Select how often the interest is compounded (e.g., Monthly, Annually).
5. Monthly Contribution: Enter the amount you plan to add to your investment each month.

Real-World Example

You start with an investment of $10,000. You plan to contribute $200 per month for 25 years. You expect an average annual return of 8%, compounded monthly.

• After 25 years, your initial $10,000 would grow to approximately $73,401.
• Your monthly contributions of $200 would grow to approximately $190,042.
• Total Future Value: $263,443.
• Of this, your total contributions were $10,000 (initial) + $60,000 (monthly) = $70,000. The remaining $193,443 is from compound interest!

Frequently Asked Questions (FAQ)

• What is the difference between APR and APY? APR (Annual Percentage Rate) is the simple interest rate. APY (Annual Percentage Yield) accounts for compounding and represents the true rate of return in a year. Higher compounding frequency leads to a higher APY.
• What is a realistic rate of return? Historically, the stock market (e.g., S&P 500) has averaged around 7-10% annually over the long term, though past performance is not a guarantee of future results.
• How important is the compounding frequency? More frequent compounding (e.g., daily vs. annually) results in slightly more interest, but the effect is less dramatic than changes in the interest rate or the length of time invested.