Julio invests 5,629 in a retire memo account with a fixed annual interest rate 9% comp ounded 6 times per finat will the acc mill nt balance be after 17 years?

To solve this problem, we need to use the formula for compound interest:<br /><br />\[ A = P \left(1 + \frac{r}{n}\right)^{nt} \]<br /><br />Where:<br />- \( A \) is the amount of money accumulated after \( n \) years, including interest.<br />- \( P \) is the principal amount (the initial amount of money).<br />- \( r \) is the annual interest rate (in decimal).<br />- \( n \) is the number of times that interest is compounded per year.<br />- \( t \) is the time the money is invested for in years.<br /><br />Given:<br />- \( P = \$5,629 \)<br />- \( r = 9\% = 0.09 \)<br />- \( n = 6 \) (since the interest is compounded 6 times per year)<br />- \( t = 17 \) years<br /><br />Now, plug these values into the formula:<br /><br />\[ A = 5629 \left(1 + \frac{0.09}{6}\right)^{6 \times 17} \]<br /><br />First, calculate the term inside the parentheses:<br /><br />\[ 1 + \frac{0.09}{6} = 1 + 0.015 = 1.015 \]<br /><br />Next, raise this term to the power of \( 6 \times 17 \):<br /><br />\[ 1.015^{102} \approx 3.073 \]<br /><br />Finally, multiply this result by the principal amount \( P \):<br /><br />\[ A = 5629 \times 3.073 \approx 17188.57 \]<br /><br />So, the account balance after 17 years will be approximately \$17,188.57.