Compound Interest Calculator

Inputs:

• Beginning Value: The initial amount of money invested or saved.
• Contribution: The amount of money added to the investment or savings on a regular basis.
• Contribution Frequency: Determines whether contributions are made monthly or annually.
• Number of Years: The duration over which the investment will grow.
• Annual Growth Rate (%): The expected annual rate of return on the investment.
• Compounding Frequency: Specifies how often the investment’s growth is calculated and added to the principal amount, either monthly or annually.

Outputs:

• Future Value: The total value of the investment at the end of the specified period.
• Growth: The total amount by which the investment has grown, excluding contributions.
• Total Contributions: The sum of the initial investment and all contributions made over the period.
• Detailed Breakdown: A table showing the beginning balance, cumulative contributions, cumulative growth, and the total for each period.
• Chart: A visual representation of the investment’s growth, contributions, and beginning balance over time.

Compound interest is a financial concept that describes the process by which an investment or deposit grows over time, as interest is added to the original principal amount, and this new total amount earns additional interest in subsequent periods. This mechanism allows the investment to grow at an accelerating rate, rather than linearly, because interest is earned on both the initial principal and the accumulated interest from previous periods.

How Compound Interest Works

To understand compound interest, consider a simple example: You deposit $1,000 in a savings account with an annual interest rate of 5%, compounded annually. After the first year, you earn interest of 5% on your $1,000, which is $50, making your total balance $1,050. In the second year, you earn 5% not just on your original $1,000 but on the $1,050, which amounts to $52.50 in interest, bringing your total to $1,102.50. This process continues each year, with the interest that you earn each year being added to your principal, which in turn earns more interest.

Compound interest can be calculated using the formula:

A = P(1 + r/n)^nt

where:

• A is the amount of money accumulated after n years, including interest.
• P is the principal amount (the initial amount of money).
• r is the annual interest rate (decimal).
• n is the number of times that interest is compounded per year.
• t is the time the money is invested for in years.

Compound Interest: “The 8th Wonder of the World”

Compound interest is often referred to as the “8th wonder of the world” by some, a phrase popularly attributed to Albert Einstein, though there’s no concrete evidence he actually said this. This expression highlights the seemingly magical ability of compound interest to turn a modest initial investment into a substantial sum over time, without any additional work or contribution from the investor beyond the initial investment.

The reason behind this powerful financial phenomenon is the exponential growth it facilitates. As interest accumulates, it generates its own interest, leading to growth that accelerates over time. This effect is most pronounced over long periods, making compound interest a cornerstone of long-term saving and investment strategies.

The chart below illustrates the power of compound interest over time. It shows the value of a single $20,000 investment growing at 8% over time. Note the outsized growth in the later years.