Suppose that 2000 is invested at a rate of 4% , compounded annually. Assuming that no withdrawals are made,find the total amount after 6 years. Do not round any intermediate computations, and round your answer to the nearest cent. Ssquare

To find the total amount after 6 years, we can 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 />- \( r = 4\% = 0.04 \)<br />- \( n = 1 \) (since the interest is compounded annually)<br />- \( t = 6 \) years<br /><br />Substitute these values into the formula:<br /><br />\[ A = 2000 \left(1 + \frac{0.04}{1}\right)^{1 \cdot 6} \]<br />\[ A = 2000 \left(1 + 0.04\right)^6 \]<br />\[ A = 2000 \left(1.04\right)^6 \]<br /><br />Now, calculate \( (1.04)^6 \):<br /><br />\[ (1.04)^6 \approx 1.2653 \]<br /><br />Then multiply by the principal amount:<br /><br />\[ A = 2000 \times 1.2653 \]<br />\[ A \approx 2530.60 \]<br /><br />So, the total amount after 6 years is approximately \( \$2530.60 \).