The principal \( P \) is borrowed at simple interest rate \( r \) for a period of time \( t \). Find the loan's future value, \( A \), or the total amount due at time \( t \). \( P=\$ 26,000, r=7.5 \%, t=5 \) years The future value is \( \$ 35,750 \). (Simplify your answer. Type an integer or a decimal.)

To find the future value \( A \) using simple interest, you can use the formula: \[ A = P + I \] where \( I \) (interest) is calculated as: \[ I = P \times r \times t \] First, convert the interest rate from percentage to decimal: \[ r = 7.5\% = 0.075 \] Now, plug in the values: \[ I = 26,000 \times 0.075 \times 5 = 9,750 \] Finally, substitute \( I \) back into the future value equation: \[ A = 26,000 + 9,750 = 35,750 \] Fun fact: Simple interest is one of the oldest forms of finance known to humanity, used as far back as ancient Mesopotamia! It's fascinating to see how these fundamental concepts have endured through time, continuing to shape our everyday financial transactions. When borrowing money, always remember to account for the total repayment amount, not just the principal. It's common to overlook the impact of the interest over time. A little planning ensures you're never caught off guard at the end of your loan term!