570 is invested at an interest rate of 4% per year and is compounded cont continuously, how much will the investment be worth in 10 years? Use the continuous compound Interest formula: A=Pe^rt. 593.26 655.66 726.74 850.34

To find the value of the investment after 10 years, we can use the continuous compound interest formula:<br /><br />\[ A = Pe^{rt} \]<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 />- \( t \) is the time the money is invested for in years.<br />- \( e \) is the base of the natural logarithm, approximately equal to 2.71828.<br /><br />Given:<br />- \( P = \$570 \)<br />- \( r = 4\% = 0.04 \)<br />- \( t = 10 \) years<br /><br />Plugging these values into the formula, we get:<br /><br />\[ A = 570 \times e^{0.04 \times 10} \]<br /><br />First, calculate the exponent:<br /><br />\[ 0.04 \times 10 = 0.4 \]<br /><br />Next, find \( e^{0.4} \):<br /><br />\[ e^{0.4} \approx 1.49182 \]<br /><br />Now multiply this by the principal amount:<br /><br />\[ A = 570 \times 1.49182 \approx 853.66 \]<br /><br />Therefore, the investment will be worth approximately \$853.66 in 10 years. The closest option to this value is:<br /><br />$\$ 850.34$<br /><br />So, the correct answer is:<br /><br />$\$ 850.34$