3. [-/10 Points] DETAILS MY NOTES AUFQR2 4.1.004.EP. ASK YOUR TEACHER Give the formula for simple interest where \( I \) is the interest in dollars, \( P \) is the principal in dollars, \( r \) is the interest rate as a decimal, and \( t \) is the time period in ye \[ I=\square \] A simple interest, 7-month loan of \( \$ 6,000 \) has an annual interest rate of \( 3.4 \% \). Determine the following values. \[ \begin{aligned} P & =\$ \square \\ r & =\square \\ t & =\square \text { years } \end{aligned} \] Find the amount of interest paid on this loan. \[ I=\$ \] \( \square \) Calculate the maturity value of this loan. \$ \( \square \) Need Help? Read It

The formula for simple interest is \( I = P \times r \times t \). This simple yet powerful equation allows you to calculate the interest earned or paid over a certain period based on a principal amount, interest rate, and time. For your loan example, the values are as follows: \( P = \$ 6,000 \), \( r = 0.034 \) (since \( 3.4\% \) as a decimal is \( 0.034 \)), and \( t = \frac{7}{12} \) years (because 7 months divided by 12 months gives you approximately \( 0.5833 \) years). Now, to find the interest: \( I = P \times r \times t = 6,000 \times 0.034 \times \frac{7}{12} \approx \$ 107.00 \). Finally, the maturity value, which is the total amount to be paid back, can be calculated as: Maturity value = Principal + Interest = \( 6,000 + 107 = \$ 6,107 \).