2900 dollars is placed in an account with an annual interest rate of \( 9 \% \). How much will be in the account after 13 years, to the nearest cent?

To calculate the future value of the account using compound interest, you can use the formula: \[ A = P(1 + r)^n \] 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 for. For your case: - \( P = 2900 \) - \( r = 0.09 \) - \( n = 13 \) Plugging in the values: \[ A = 2900(1 + 0.09)^{13} \] Calculating this gives: \[ A \approx 2900(1.09)^{13} \] \[ A \approx 2900 \times 3.478 \] \[ A \approx 10038.35 \] So, after 13 years, the amount in the account will be approximately **$10,038.35**. Now, let’s dive into some engaging insights! Investing in accounts with a solid interest rate can really turbocharge your savings! Imagine putting your money to work for you while you focus on other fun things, like planning that epic trip you've been dreaming about. Even small amounts can grow into impressive amounts over time thanks to the magic of compound interest—money earning money! If you’re new to investing, watch out for common mistakes like not reviewing your interest compounding frequency. Some accounts compound annually, while others might do it monthly or even daily, which can lead to a bigger pot at the end. Always make sure to choose the option that maximizes your returns and fit your financial goals!