Ted invests 5,670 in a savings account with a fixed annual interest rate of 4% compounded 4 times per year will the account balance be after 4 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 />- \( P = \$5,670 \)<br />- \( r = 4\% = 0.04 \)<br />- \( n = 4 \) (since the interest is compounded 4 times per year)<br />- \( t = 4 \) years<br /><br />Now, plug these values into the formula:<br /><br />\[ A = 5670 \left(1 + \frac{0.04}{4}\right)^{4 \times 4} \]<br /><br />First, calculate the term inside the parentheses:<br /><br />\[ \frac{0.04}{4} = 0.01 \]<br /><br />So,<br /><br />\[ 1 + 0.01 = 1.01 \]<br /><br />Next, raise this to the power of \( 4 \times 4 = 16 \):<br /><br />\[ 1.01^{16} \approx 1.16985856 \]<br /><br />Finally, multiply this by the principal amount \( P \):<br /><br />\[ A = 5670 \times 1.16985856 \approx 6605.23 \]<br /><br />Therefore, the account balance after 4 years will be approximately \$6,605.23.