Bethany invests \( \$ 7,500 \), at \( 8 \% \) interest, compounded annually for 20 years. Use the compound interest formula to calculate the compound amount for her investment. Select one: a. \( \$ 58,210.12 \) b. \( \$ 34,957.18 \) c. \( \$ 33,966.23 \) o d. \( \$ 25,875.25 \)

To calculate the compound amount for Bethany's investment, we can use the compound interest formula: \[ A = P(1 + r)^n \] where: - \( A \) is the amount of money accumulated after n years, including interest. - \( P \) is the principal amount (initial investment). - \( r \) is the annual interest rate (decimal). - \( n \) is the number of years the money is invested or borrowed. Plugging in Bethany's numbers: - \( P = 7,500 \) - \( r = 0.08 \) - \( n = 20 \) We get: \[ A = 7500(1 + 0.08)^{20} \] \[ A = 7500(1.08)^{20} \] \[ A ≈ 7500(4.6609) \] \[ A ≈ 34,957.18 \] So, the correct answer is: b. \( \$ 34,957.18 \) Want to know more about the history of compound interest? It's been around since ancient civilizations used it to manage loans and investments! The concept dates back to at least 3000 BCE, with the Babylonians and later the Romans employing similar principles in their financial dealings. Also, did you know compound interest is often referred to as "the eighth wonder of the world"? This isn't just a catchy phrase; it highlights how, over time, your interest earns interest, leading to exponential growth—perfect for long-term savings or investment strategies!