c. What rate per year must be paid for a principal of \( \$ 750 \) to earn interest of \( \$ 180 \) in 4 years?

To find the rate per year that must be paid for a principal of \( \$750 \) to earn \( \$180 \) in interest over 4 years, we can use the formula for simple interest: \[ I = P \times r \times t \] where: - \( I \) is the interest earned, - \( P \) is the principal amount, - \( r \) is the rate of interest per year (as a decimal), - \( t \) is the time in years. Given: - \( I = 180 \) - \( P = 750 \) - \( t = 4 \) We can rearrange the formula to solve for \( r \): \[ r = \frac{I}{P \times t} \] Substituting the known values into the equation: \[ r = \frac{180}{750 \times 4} \] Calculating the denominator: \[ 750 \times 4 = 3000 \] Now substituting back into the equation for \( r \): \[ r = \frac{180}{3000} \] Calculating \( r \): \[ r = 0.06 \] To express \( r \) as a percentage, we multiply by 100: \[ r = 0.06 \times 100 = 6\% \] Thus, the rate per year that must be paid is \( \boxed{6\%} \).