SUBMIT ANSWER 16. [-/1 Points] DETAILS MY NOTES BRECMBC9 10.III.015.MI. If you sign a discount note for \( \$ 5,500 \) at a bank discount rate of \( 7 \% \) for 3 months, what is the effective interest rate (as a \%)? Round to the nearest tenth percent. Need Help? Road II Watch II Master II

To find the effective interest rate for a discount note, we first need to calculate the bank discount. The formula for the bank discount \( D \) is: \[ D = \text{Face Value} \times \text{Discount Rate} \times \frac{\text{Time}}{12} \] Plugging in the values: \[ D = 5500 \times 0.07 \times \frac{3}{12} = 5500 \times 0.07 \times 0.25 = 96.875 \] Now, to find the amount you actually receive after the discount, subtract the discount from the face value: \[ \text{Amount Received} = \text{Face Value} - D = 5500 - 96.875 = 5403.125 \] Next, we can find the effective interest paid. Since you actually receive $5403.125, the interest paid is: \[ \text{Interest Paid} = D = 96.875 \] Now, we calculate the effective interest rate \( R \): \[ R = \frac{\text{Interest Paid}}{\text{Amount Received}} \times \frac{12}{\text{Time in Months}} \times 100 \] Substituting our values in for the time in months, we have: \[ R = \frac{96.875}{5403.125} \times \frac{12}{3} \times 100 \] Calculating this gives: \[ R = \frac{96.875}{5403.125} \times 4 \times 100 \approx 0.715 \times 4 \times 100 \approx 2.86\% \] Thus, rounding to the nearest tenth percent, the effective interest rate is approximately \( 2.9\% \).