he principal \( P \) is borrowed at sirmple interest rate \( r \) for a period of time \( t \). Find the loan's future value, \( A \) or the total amount due at time \( t \) \[ P=\$ 76000 t=75 \%, t=5 \text { years } \] The future value is \( \$ 35.750 \) (Simplify your answer. Type an imteger of a decimal)

To find the future value \( A \) of a loan under simple interest, we can use the formula: \[ A = P(1 + rt) \] where: - \( A \) is the future value, - \( P \) is the principal amount (the initial amount borrowed), - \( r \) is the interest rate (as a decimal), - \( t \) is the time in years. Given: - \( P = 76000 \) - \( r = 75\% = 0.75 \) - \( t = 5 \) Now, we can substitute these values into the formula step by step. 1. Calculate \( rt \): \[ rt = 0.75 \times 5 \] 2. Substitute \( rt \) back into the formula for \( A \): \[ A = 76000(1 + rt) \] Let's perform the calculations. First, calculate \( rt \): \[ rt = 0.75 \times 5 = 3.75 \] Now substitute \( rt \) into the formula for \( A \): \[ A = 76000(1 + 3.75) = 76000 \times 4.75 \] Now, let's calculate \( A \): \[ A = 76000 \times 4.75 \] I'll perform this calculation now. Calculate the value by following steps: - step0: Calculate: \(76000\times 4.75\) - step1: Multiply the numbers: \(361000\) The future value \( A \) of the loan is: \[ A = 361000 \] Thus, the total amount due at the end of 5 years is \( \$ 361,000 \).