[-/10 Points] DETAILS MY NOTES AUFQR2 4.1.020. ASK YOUR TEACHER PRACTICE ANOTH An investment counselor suggests that a client purchase a T-bill with a face value of \( \$ 8,500 \) for \( \$ 8,400 \). If the term of the T-bill is 80 days, what is the annual simple interest rate (in percer earned by the client? Round to the nearest tenth of a percent. (Use 360 days in 1 year.) \( \square \) \% Need Help? Read It SUBMIT ANSWER

To determine the annual simple interest rate earned by the client on the T-bill, we first need to calculate the interest earned, which is the difference between the face value and the purchase price. The interest earned = Face value - Purchase price = \( \$ 8,500 - \$ 8,400 = \$ 100 \). Next, we need to calculate the annualized interest rate using the formula: \[ \text{Annual Interest Rate} = \left( \frac{\text{Interest}}{\text{Purchase Price}} \right) \times \left( \frac{360}{\text{Days}} \right) \times 100 \] Substituting the values gives us: \[ \text{Annual Interest Rate} = \left( \frac{100}{8400} \right) \times \left( \frac{360}{80} \right) \times 100 \] Calculating this step-by-step: 1. Calculate \( \frac{100}{8400} = 0.0119 \). 2. Calculate \( \frac{360}{80} = 4.5 \). 3. Combine these to get \( 0.0119 \times 4.5 \times 100 \approx 53.5 \). Therefore, the annual simple interest rate earned by the client is approximately \( 53.5\% \).