Suppose Maji borrowed \( \$ 3,923.00 \), but you forgot what the interest rate was for the simple interest loan. If Maji ended up paying \( \$ 7,100.63 \) in total after 9 years. What was the interest rate of the loan? Record the rate as a percentage rounded to the nearest percent.
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To find the interest rate of the loan, we can use the formula for simple interest: \[ A = P(1 + rt) \] where: - \( A \) is the total amount paid, - \( P \) is the principal amount (initial loan), - \( r \) is the interest rate (as a decimal), - \( t \) is the time in years. In this case, we know: - \( A = 7,100.63 \) - \( P = 3,923.00 \) - \( t = 9 \) We need to solve for \( r \): \[ 7,100.63 = 3,923 \times (1 + 9r) \] First, divide both sides by 3,923: \[ \frac{7,100.63}{3,923} = 1 + 9r \] Calculating the left side: \[ 1.81013 \approx 1 + 9r \] Now, subtract 1 from both sides: \[ 0.81013 = 9r \] Finally, divide by 9: \[ r = \frac{0.81013}{9} \approx 0.09001 \] To convert the decimal to a percentage, multiply by 100: \[ r \approx 9.00\% \] Rounding to the nearest percent, the interest rate is approximately **9%**.