c. Taylor invests \( \$ 4250 \) and receives \( \$ 5525 \) in total with a \( 5 \% \) interest rate. How long must he have had the money invested? \[ 4250(.05)(t) \]

To find out how long Taylor must have had the money invested, we can use the formula for simple interest: \[ A = P + I \] where: - \( A \) is the total amount received, - \( P \) is the principal amount (initial investment), - \( I \) is the interest earned. The interest \( I \) can be calculated using the formula: \[ I = P \cdot r \cdot t \] where: - \( r \) is the interest rate (as a decimal), - \( t \) is the time in years. Given: - \( A = 5525 \) - \( P = 4250 \) - \( r = 0.05 \) First, we can find the interest earned \( I \): \[ I = A - P = 5525 - 4250 = 1275 \] Now we can set up the equation for interest: \[ 1275 = 4250 \cdot 0.05 \cdot t \] Now, simplify the right side: \[ 1275 = 212.5 \cdot t \] Next, solve for \( t \): \[ t = \frac{1275}{212.5} \] Calculating this gives: \[ t = 6 \] Thus, Taylor must have had the money invested for **6 years**.