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(1 + 0.05)^12: Understanding the Concept of Compound Interest
In finance and economics, compound interest is a crucial concept that helps us understand how investments grow over time. One way to illustrate this concept is by examining the expression (1 + 0.05)^12. In this article, we'll break down this expression and explore its significance in finance.
What does the expression represent?
The expression (1 + 0.05)^12 represents the result of compounding an investment over 12 periods at an interest rate of 5% per period. Let's break it down:
1represents the principal amount, which is the initial investment.0.05represents the interest rate, which is 5% or 0.05 in decimal form.^12represents the number of periods, which is 12 in this case.
How does compound interest work?
Compound interest is the concept of earning interest on both the principal amount and any accrued interest over time. In other words, the interest earned in one period becomes the principal for the next period, generating even more interest.
To illustrate this, let's consider a simple example:
Suppose you invest $100 at an annual interest rate of 5%. At the end of the first year, you'll have earned $5 in interest, making your total balance $105.
In the second year, you'll earn 5% interest on the new balance of $105, not just the initial $100. This means you'll earn $5.25 in interest (5% of $105), bringing your total balance to $110.25.
As you can see, the interest earned in one period becomes the principal for the next period, resulting in exponential growth over time.
Calculating the result of (1 + 0.05)^12
Using a calculator or computer program, we can calculate the result of (1 + 0.05)^12:
(1 + 0.05)^12 ≈ 1.79585
This means that if you invest $100 at an annual interest rate of 5%, compounded annually for 12 years, your investment will grow to approximately $179.59.
Conclusion
The expression (1 + 0.05)^12 represents the power of compound interest in finance. By understanding how interest is compounded over time, investors can make informed decisions about their investments and watch their wealth grow exponentially.
