Compound Interest Formula Example With Solution Pdf

Understanding the Compound Interest Formula: Examples and Solutions

Understanding compound interest is crucial for anyone looking to build long-term wealth through savings or investments. This article will break down the compound interest formula, provide clear examples with step-by-step solutions, and offer resources for further learning. This guide will help you confidently calculate the power of compounding and make informed financial decisions.

What is Compound Interest?

Compound interest is the interest earned on both the principal amount and the accumulated interest from previous periods. Unlike simple interest, which only calculates interest on the principal, compound interest grows exponentially over time, creating a snowball effect that significantly increases your returns. This makes it a powerful tool for long-term financial growth.

The Compound Interest Formula

The formula for calculating compound interest is:

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

Where:

• A = the future value of the investment/loan, including interest
• P = the principal investment amount (the initial deposit or loan amount)
• r = the annual interest rate (decimal)
• n = the number of times that interest is compounded per year
• t = the number of years the money is invested or borrowed for

Example 1: Annual Compounding

Let's say you invest $1,000 (P) at an annual interest rate of 5% (r) for 3 years (t), compounded annually (n=1). What will be the future value of your investment?

Solution:

1. Plug the values into the formula: A = 1000 (1 + 0.05/1)^(1*3)
2. Simplify: A = 1000 (1 + 0.05)^3
3. Calculate: A = 1000 (1.05)^3 = 1000 * 1.157625 ≈ $1157.63

Therefore, after 3 years, your investment will be worth approximately $1157.63.

Example 2: Quarterly Compounding

Now let's consider the same investment but with quarterly compounding (n=4).

Solution:

1. Plug the values into the formula: A = 1000 (1 + 0.05/4)^(4*3)
2. Simplify: A = 1000 (1 + 0.0125)^12
3. Calculate: A = 1000 (1.0125)^12 ≈ $1160.75

Notice that with quarterly compounding, your investment grows slightly faster, reaching approximately $1160.75 after 3 years. This highlights the impact of compounding frequency.

Example 3: Monthly Compounding

Let’s explore the impact of even more frequent compounding. We'll use the same principal, interest rate and time, but now compound monthly (n=12).

Solution:

1. Plug the values into the formula: A = 1000 (1 + 0.05/12)^(12*3)
2. Simplify: A = 1000 (1 + 0.004167)^36
3. Calculate: A = 1000 (1.004167)^36 ≈ $1161.47

As you can see, more frequent compounding leads to slightly higher returns.

Key Takeaways:

• The power of compounding: Even small increases in interest rates or compounding frequency can significantly impact your returns over time.
• Long-term investment: The longer your money is invested, the greater the impact of compounding.
• Understanding the formula: Familiarizing yourself with the formula empowers you to calculate the potential growth of your investments or loans.

This article provides a basic understanding of compound interest calculations. More complex scenarios might involve varying interest rates or additional contributions. Remember that this information is for educational purposes and does not constitute financial advice. Always consult with a financial professional before making any significant investment decisions.