Question Dale takes out a loan of \( \$ 8,000 \) with a \( 15.2 \% \) interest rate that is compounded semi-annually. If he pays off the loan in 3 years, how much will he end up paying? Round your answer to the nearest cent. Do NOT round until you have calculated the final answer.

To calculate the total amount Dale will pay at the end of 3 years, we can use the formula for compound interest: \[ A = P \left(1 + \frac{r}{n}\right)^{nt} \] Where: - \( A \) is the amount of money accumulated after n years, including interest. - \( P \) is the principal amount (the initial amount of money). - \( r \) is the annual interest rate (decimal). - \( n \) is the number of times that interest is compounded per year. - \( t \) is the number of years the money is borrowed. Given: - \( P = 8000 \) - \( r = 0.152 \) - \( n = 2 \) (since interest is compounded semi-annually) - \( t = 3 \) Now, plug in the values: \[ A = 8000 \left(1 + \frac{0.152}{2}\right)^{2 \cdot 3} \] Calculate: \[ A = 8000 \left(1 + 0.076\right)^{6} \] \[ A = 8000 \left(1.076\right)^{6} \] \[ A = 8000 \cdot 1.484812 \] \[ A \approx 11878.50 \] Therefore, Dale will end up paying approximately \( \$ 11,878.50 \) when he pays off the loan in 3 years.