29. Marcus borrowed \( \$ 9,000 \) from his bank to buy a car. The bank charged him a simple interest rate of \( 1.25 \% \). By the time he paid back the money, he had paid a total of \( \$ 9,281.25 \). How long did it take Marcus to pay back the money?

To find out how long it took Marcus to pay back the money, we can use the formula for simple interest: \[ A = P + I \] where: - \( A \) is the total amount paid back, - \( P \) is the principal amount (the initial amount borrowed), - \( I \) is the interest paid. The interest \( I \) can also be calculated using the formula: \[ I = P \times r \times t \] where: - \( r \) is the interest rate (as a decimal), - \( t \) is the time in years. Given: - \( A = 9,281.25 \) - \( P = 9,000 \) - \( r = 1.25\% = 0.0125 \) First, we can find the interest \( I \): \[ I = A - P = 9,281.25 - 9,000 = 281.25 \] Now we can substitute \( I \) into the interest formula: \[ 281.25 = 9,000 \times 0.0125 \times t \] Now, we can solve for \( t \): \[ 281.25 = 112.5 \times t \] Dividing both sides by \( 112.5 \): \[ t = \frac{281.25}{112.5} = 2.5 \] Thus, it took Marcus **2.5 years** to pay back the money.