- In 2008, the last baseball hit for a home run by Barry. Bonds was auctioned off for about 376,000 The price of the ball was considered a bargain, in part because potential buyer were unsure if Bonds would play again. Experts on such collectibles often argue that collectibles such as this will double in value over a 10-year period. Question: What is the return on investment each year over the 10-year period?

To calculate the return on investment (ROI) each year over the 10-year period, we need to first determine the future value of the baseball after 10 years, assuming it doubles in value.<br /><br />Let's denote the initial price of the baseball as \( P \) and the final price after 10 years as \( F \).<br /><br />Given:<br />- Initial price, \( P = \$376,000 \)<br />- Final price after 10 years, \( F = 2P = 2 \times \$376,000 = \$752,000 \)<br /><br />We can use the formula for compound interest to find the annual return rate \( r \):<br /><br />\[ F = P \times (1 + r)^n \]<br /><br />Where:<br />- \( F \) is the future value<br />- \( P \) is the present value (initial price)<br />- \( r \) is the annual return rate<br />- \( n \) is the number of years<br /><br />Plugging in the values:<br /><br />\[ \$752,000 = \$376,000 \times (1 + r)^{10} \]<br /><br />Divide both sides by \$376,000:<br /><br />\[ 2 = (1 + r)^{10} \]<br /><br />Take the 10th root of both sides to solve for \( 1 + r \):<br /><br />\[ 1 + r = 2^{1/10} \]<br /><br />\[ 1 + r \approx 1.0718 \]<br /><br />So,<br /><br />\[ r \approx 0.0718 \]<br /><br />Convert the decimal to a percentage:<br /><br />\[ r \approx 7.18\% \]<br /><br />Therefore, the annual return on investment over the 10-year period is approximately 7.18%.