Suppose that 2000 is invested at a rate of 3.3% compounded quarterly. Assuming that no withdrawals are made,find the total amount after 7 years. Do not round any intermediate computations, and round your answer to the nearest cent.

To solve this problem, we will 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 (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 />- \( P = \$2000 \)<br />- \( r = 3.3\% = 0.033 \)<br />- \( n = 4 \) (since the interest is compounded quarterly)<br />- \( t = 7 \) years<br /><br />Now, plug these values into the formula:<br /><br />\[ A = 2000 \left(1 + \frac{0.033}{4}\right)^{4 \cdot 7} \]<br /><br />First, calculate the quarterly interest rate:<br /><br />\[ \frac{0.033}{4} = 0.00825 \]<br /><br />Next, add 1 to the quarterly interest rate:<br /><br />\[ 1 + 0.00825 =.00825 \]<br /><br />Then, raise this to the power of \( 4 \times 7 = 28 \):<br /><br />\[ 1.00825^{28} \approx 1.26824 \]<br /><br />Finally, multiply this by the principal amount:<br /><br />\[ A = 2000 \times 1.26824 \approx 2536.48 \]<br /><br />So, the total amount after 7 years is approximately \$2536.48.