II \( \$ 15000 \) is invested at \( 12 \% \) interest compounded monthly, fond the interest earned in 15 years The interest eamed in 15 years is \( 3 \square \) (Do not round until the linat answer Then round to two decinal places as needed)

To calculate the interest earned on an investment compounded monthly, 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 invested or borrowed. Given: - \( P = 15000 \) - \( r = 0.12 \) (12% as a decimal) - \( n = 12 \) (compounded monthly) - \( t = 15 \) Now, we can plug in the values: \[ A = 15000 \left(1 + \frac{0.12}{12}\right)^{12 \times 15} \] Calculating the values step by step: 1. Calculate \( \frac{r}{n} \): \[ \frac{0.12}{12} = 0.01 \] 2. Calculate \( nt \): \[ 12 \times 15 = 180 \] 3. Now substitute these values back into the formula: \[ A = 15000 \left(1 + 0.01\right)^{180} \] 4. Calculate \( (1 + 0.01)^{180} \): \[ (1.01)^{180} \approx 6.116 \] 5. Now calculate \( A \): \[ A \approx 15000 \times 6.116 \approx 91740 \] 6. Finally, to find the interest earned, subtract the principal from the total amount: \[ \text{Interest} = A - P = 91740 - 15000 = 76740 \] Thus, the interest earned in 15 years is approximately: \[ \text{Interest} \approx 76740 \] So, the interest earned in 15 years is \( 76740 \).