Texas Instruments Financial Calculator

Investment Growth Calculator

Understanding Compound Interest

Compound interest is often called the "eighth wonder of the world." It's a powerful concept in finance that describes how an investment or loan grows over time, not just on the initial amount invested (principal), but also on the accumulated interest from previous periods. Essentially, your interest starts earning interest, leading to exponential growth.

The Compound Interest Formula

The mathematical formula used to calculate the future value of an investment with compound interest is:

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

Where:

• FV is the Future Value of the investment/loan, including interest
• P is the Principal amount (the initial amount of money)
• r is the Annual interest rate (as a decimal)
• n is the number of times that interest is compounded per year
• t is the number of years the money is invested or borrowed for

How This Calculator Works

This calculator takes the following inputs and applies the compound interest formula:

• Initial Investment ($P$): The starting amount of money you invest.
• Annual Interest Rate (%): The yearly rate at which your investment grows. This is converted to a decimal (e.g., 7.5% becomes 0.075) for the calculation.
• Compounding Periods Per Year ($n$): How frequently the interest is calculated and added to the principal. Common examples include:
  • Annually (n=1)
  • Semi-annually (n=2)
  • Quarterly (n=4)
  • Monthly (n=12)
  • Daily (n=365)
• Number of Years ($t$): The duration for which the investment will grow.

The calculator then computes the Future Value ($FV$), showing you the total amount your initial investment will grow to after the specified time, considering the effects of compounding.

Use Cases for Compound Interest Calculation

Understanding compound interest is crucial for various financial planning scenarios:

• Long-Term Investments: Estimating the future value of retirement funds, stocks, bonds, or mutual funds.
• Savings Goals: Determining how much an initial savings deposit might grow over time for large purchases like a house down payment or education costs.
• Understanding Loans: While this calculator focuses on growth, the same principles apply to how loans accumulate interest (though often calculated differently).
• Financial Education: Demonstrating the power of starting early and the impact of different interest rates and compounding frequencies.

Example Calculation

Let's consider an example:

• Initial Investment (P): $10,000
• Annual Interest Rate: 8% (r = 0.08)
• Compounding Periods Per Year (n): 12 (monthly)
• Number of Years (t): 20

Plugging these into the formula:

FV = 10000 * (1 + 0.08/12)^(12*20)

FV = 10000 * (1 + 0.006666...)^(240)

FV = 10000 * (1.006666...)^(240)

FV ≈ 10000 * 4.9268

FV ≈ $49,268

This shows that an initial investment of $10,000 could grow to approximately $49,268 over 20 years with monthly compounding at an 8% annual rate. This highlights the significant benefit of consistent investment and the magic of compounding over long periods.