2. A brand new 2024 Toyota Tundra starts at a MSRP of 71,537.00 Toyota have an average annual depreciation rate of 2.0465% What is the value of the truck at the end of a six year loan? Round to the nearest penny.

To calculate the value of the 2024 Toyota Tundra at the end of a six-year loan, we need to use the formula for exponential decay:<br /><br />\[ V = P \times (1 - r)^t \]<br /><br />Where:<br />- \( V \) is the final value<br />- \( P \) is the initial value (MSRP)<br />- \( r \) is the annual depreciation rate (as a decimal)<br />- \( t \) is the number of years<br /><br />Given:<br />- \( P = \$71,537.00 \)<br />- \( r = 2.0465\% = 0.020465 \)<br />- \( t = 6 \)<br /><br />Now, plug these values into the formula:<br /><br />\[ V = 71,537 \times (1 - 0.020465)^6 \]<br /><br />First, calculate \( 1 - 0.020465 \):<br /><br />\[ 1 - 0.020465 = 0.979535 \]<br /><br />Next, raise this to the power of 6:<br /><br />\[ 0.979535^6 \approx 0.911 \]<br /><br />Finally, multiply by the initial value:<br /><br />\[ V = 71,537 \times 0.911 \approx 65,073.57 \]<br /><br />So, the value of the truck at the end of a six-year loan is approximately \$65,073.57.