Mark took a loan out for 25,690 to purchase a truck.At an interest rate of 5.2% compounded monthly, how much total will he have paid after 5 years? 34,710.88 flipping pancakes 33,672.68 climbing trees 33,299.42 playing dodgeball 34,157.04 riding unicycles

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 \( t \) years, including interest.<br />- \( P \) is the principal amount (the initial amount of money).<br />- \( r \) is the annual interest rate (in decimal form).<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 />- \( P = \$25,690 \)<br />- \( r = 5.2\% = 0.052 \)<br />- \( n = 12 \) (since the interest is compounded monthly)<br />- \( t = 5 \) years<br /><br />Plugging these values into the formula:<br /><br />\[ A = 25690 \left(1 + \frac{0.052}{12}\right)^{12 \times 5} \]<br /><br />First, calculate the monthly interest rate:<br /><br />\[ \frac{0.052}{12} = 0.0043333 \]<br /><br />Next, add 1 to the monthly interest rate:<br /><br />\[ 1 + 0.0043333 = 1.0043333 \]<br /><br />Then, raise this to the power of the total number of compounding periods (12 months * 5 years):<br /><br />\[ 1.0043333^{60} \approx 1.283682 \]<br /><br />Finally, multiply this by the principal amount:<br /><br />\[ A = 25690 \times 1.283682 \approx 33,299.42 \]<br /><br />So, the total amount Mark will have paid after 5 years is:<br /><br />\[ \boxed{33,299.42} \]<br /><br />Therefore, the correct answer is:<br /><br />\[ \boxed{\$33,299.42 \text{ playing dodgeball}} \]