You deposit \( \$ 400 \) in an account earning \( 5 \% \) interest compounded annually. How much will you have in the account in 20 years? Round value to the nearest cent.

To find out how much you'll have in the account after 20 years, we can use the formula for compound interest: \[ A = P(1 + r)^t \] Where: - \( A \) is the amount of money accumulated after n years, including interest. - \( P \) is the principal amount (the initial deposit or investment). - \( r \) is the annual interest rate (decimal). - \( t \) is the number of years the money is invested or borrowed. Plugging in the values: - \( P = 400 \) - \( r = 0.05 \) - \( t = 20 \) Calculate: \[ A = 400(1 + 0.05)^{20} \] \[ A = 400(1.05)^{20} \] \[ A \approx 400 \times 2.6533 \) (using a calculator for \( (1.05)^{20} \)) \] \[ A \approx 1061.32 \] Thus, you will have approximately **$1,061.32** in the account after 20 years. --- Did you know that the concept of compound interest dates back to ancient civilizations? The Babylonians and Greeks practiced early forms of lending with interest, but it wasn’t until the Renaissance that compound interest became a formal concept in Europe, enabling investors to grow their wealth more rapidly! If you're planning to invest for the future, remember that starting early and allowing your money to compound over a long period can significantly increase your returns. However, be cautious about fees and penalties that could eat away at your compounded earnings! Always read the fine print on any investment account you choose.