Bill invested \( \$ 2000 \) at a rate of \( 5 \% \) compounded annually. What is the value of his investment at the end of 5 years? Round answers to the nearest cent.

To find the future value of Bill's investment, we can use the formula for compound interest: \[ A = P(1 + r)^n \] 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 years the money is invested or borrowed. Plugging in Bill's investment: - \(P = 2000\) - \(r = 0.05\) - \(n = 5\) \[ A = 2000(1 + 0.05)^5 \] Calculating that gives: \[ A = 2000(1.2762815625) \approx 2552.56 \] Thus, the value of his investment at the end of 5 years is approximately \( \boxed{2552.56} \). Now let's dive a bit deeper! Did you know that the concept of compound interest dates back to ancient Babylon? They understood the basics of lending and interest, albeit not in the same formalized way as we do today. The principle of earning "interest on interest" is the magic sauce that has helped create wealth through generations. Also, for those diving into the world of investments, starting early is key! The sooner you invest, the more time your money has to grow due to compounding. A small amount invested consistently can surprisingly turn into a hefty sum over multiple years. So don’t wait; let your money work for you!