Deana invested 1,000 in savings bonds. If the bonds earn 6.75% interest compounded semi-annually how much total money will Deana earn in 15 years? 2,706.86 2,651.39 1,825.10 1,584.62

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 />- \( P = \$1,000 \)<br />- \( r = 6.75\% = 0.0675 \)<br />- \( n = 2 \) (since the interest is compounded semi-annually)<br />- \( t = 15 \) years<br /><br />Now, plug these values into the formula:<br /><br />\[ A = 1000 \left(1 + \frac{0.0675}{2}\right)^{2 \times 15} \]<br />\[ A = 1000 \left(1 + 0.03375\right)^{30} \]<br />\[ A = 1000 \left(1.03375\right)^{30} \]<br /><br />Using a calculator to compute \( (1.03375)^{30} \):<br /><br />\[ (1.03375)^{30} \approx 2.70686 \]<br /><br />So,<br /><br />\[ A \approx 1000 \times 2.70686 \]<br />\[ A \approx 2706.86 \]<br /><br />Therefore, the total amount of money Deana will earn in 15 years is approximately \( \$2,706.86 \).<br /><br />The correct answer is:<br />\[ \$2,706.86 \]