4. Calculate the simple interest and the amount. a) \( \$ 2500 \) invested at an annual interest rate of \( 6 \% \) for 6 mor b) \( \$ 6000 \) invested at an annual interest rate of \( 6 \% \) for 3 year c) \( \$ 700 \) invested at an annual interest rate of \( 8 \% \) for 3 mont

To calculate the simple interest and the total amount for each investment, we can use the formula for simple interest: \[ I = P \times r \times t \] where: - \( I \) is the interest, - \( P \) is the principal amount (initial investment), - \( r \) is the annual interest rate (in decimal), - \( t \) is the time the money is invested for (in years). The total amount \( A \) after the investment period can be calculated as: \[ A = P + I \] Now, let's solve each part step by step. ### a) \( \$ 2500 \) at \( 6\% \) for \( 6 \) months 1. Convert the interest rate to decimal: \( r = \frac{6}{100} = 0.06 \). 2. Convert the time from months to years: \( t = \frac{6}{12} = 0.5 \) years. 3. Calculate the interest: \[ I = 2500 \times 0.06 \times 0.5 \] 4. Calculate the total amount: \[ A = 2500 + I \] ### b) \( \$ 6000 \) at \( 6\% \) for \( 3 \) years 1. Convert the interest rate to decimal: \( r = 0.06 \). 2. Time is already in years: \( t = 3 \). 3. Calculate the interest: \[ I = 6000 \times 0.06 \times 3 \] 4. Calculate the total amount: \[ A = 6000 + I \] ### c) \( \$ 700 \) at \( 8\% \) for \( 3 \) months 1. Convert the interest rate to decimal: \( r = \frac{8}{100} = 0.08 \). 2. Convert the time from months to years: \( t = \frac{3}{12} = 0.25 \) years. 3. Calculate the interest: \[ I = 700 \times 0.08 \times 0.25 \] 4. Calculate the total amount: \[ A = 700 + I \] Now, let's perform the calculations for each part. Calculate the value by following steps: - step0: Calculate: \(2500\times 0.06\times 0.5\) - step1: Multiply the terms: \(150\times 0.5\) - step2: Multiply the numbers: \(75\) Calculate or simplify the expression \( 700 * 0.08 * 0.25 \). Calculate the value by following steps: - step0: Calculate: \(700\times 0.08\times 0.25\) - step1: Multiply the terms: \(56\times 0.25\) - step2: Multiply the numbers: \(14\) Calculate or simplify the expression \( 6000 * 0.06 * 3 \). Calculate the value by following steps: - step0: Calculate: \(6000\times 0.06\times 3\) - step1: Multiply the terms: \(360\times 3\) - step2: Multiply the numbers: \(1080\) Calculate or simplify the expression \( 700 + 14 \). Calculate the value by following steps: - step0: Calculate: \(700+14\) - step1: Add the numbers: \(714\) Calculate or simplify the expression \( 2500 + 75 \). Calculate the value by following steps: - step0: Calculate: \(2500+75\) - step1: Add the numbers: \(2575\) Calculate or simplify the expression \( 6000 + 1080 \). Calculate the value by following steps: - step0: Calculate: \(6000+1080\) - step1: Add the numbers: \(7080\) Here are the calculations for each investment: ### a) \( \$ 2500 \) at \( 6\% \) for \( 6 \) months - **Interest**: \[ I = 2500 \times 0.06 \times 0.5 = 75 \] - **Total Amount**: \[ A = 2500 + 75 = 2575 \] ### b) \( \$ 6000 \) at \( 6\% \) for \( 3 \) years - **Interest**: \[ I = 6000 \times 0.06 \times 3 = 1080 \] - **Total Amount**: \[ A = 6000 + 1080 = 7080 \] ### c) \( \$ 700 \) at \( 8\% \) for \( 3 \) months - **Interest**: \[ I = 700 \times 0.08 \times 0.25 = 14 \] - **Total Amount**: \[ A = 700 + 14 = 714 \] ### Summary of Results: - a) Interest: \( 75 \), Total Amount: \( 2575 \) - b) Interest: \( 1080 \), Total Amount: \( 7080 \) - c) Interest: \( 14 \), Total Amount: \( 714 \)