A company lends \( \$ 1,300,000 \) for 2 years at \( 24 \% \), compounded monthly to another company that manufactures fug boats. Find (a) the future value and (b) the interest. Click the icon to view the compound interest table. (a) Future value \( =\$ \square \) (Simplify your answer.) (b) Interest \( =\$ \square \) (Simplify your answer.)

To find the future value and the interest from the given loan, we will use the compound interest formula: \[ A = P \left(1 + \frac{r}{n}\right)^{nt} \] Where: - \( A \) is the future value (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 invested or borrowed. Given: - \( P = 1,300,000 \) - \( r = 0.24 \) (24% as a decimal) - \( n = 12 \) (compounded monthly) - \( t = 2 \) Plugging the values into the formula: \[ A = 1,300,000 \left(1 + \frac{0.24}{12}\right)^{12 \times 2} \] Calculating inside the parentheses first: \[ 1 + \frac{0.24}{12} = 1 + 0.02 = 1.02 \] Next, calculate the exponent: \[ 12 \times 2 = 24 \] Now substituting back into the equation: \[ A = 1,300,000 \times (1.02)^{24} \] Calculate \((1.02)^{24}\): \[ (1.02)^{24} \approx 1.6084 \] Now, compute \( A \): \[ A \approx 1,300,000 \times 1.6084 \approx 2,090,920 \] So the future value is: (a) Future value \( = \$2,090,920 \) Now, to find the interest earned: \[ \text{Interest} = A - P \] So, we calculate: \[ \text{Interest} = 2,090,920 - 1,300,000 = 790,920 \] (b) Interest \( = \$790,920 \)