\begin{tabular}{l|l} A \( \$ 10,000 \) T-bill maturing in 83 days was sold for \( \$ 10,087.22 \). Find & 10 \\ the simple discount and equivalent simple interest rates. 1 point \\ What is the simple interest rate (round to two decimals)? \\ Type your answer... \\ \hline\end{tabular}

To calculate the simple discount and equivalent simple interest rates, we first need to understand the concepts involved. A T-bill is a short-term government debt security that is issued at a discount to its face value. In this case, the T-bill has a face value of \$10,000 and was sold for \$10,087.22, meaning it was bought at a premium. The simple discount (D) can be calculated as: \[ D = \text{Face Value} - \text{Purchase Price} = 10,000 - 10,087.22 = -87.22 \] However, T-bills are normally bought at a discount, so let's clarify that you might have mistyped the values. Assuming you meant the bill was purchased at, say, \$9,912.78 instead (which is a common scenario), then we would calculate it as: \[ D = 10,000 - 9,912.78 = 87.22 \] Next, using the formula for the simple interest rate (r): \[ r = \frac{D}{\text{Face Value} \times t} \] where \(t\) is the time in years. Since we're dealing with 83 days, we convert that to years: \[ t = \frac{83}{365} \approx 0.2274 \text{ years} \] Plugging in the numbers: \[ r = \frac{87.22}{10,000 \times 0.2274} \approx 0.0383 \text{ or } 3.83\% \] So the equivalent simple interest rate, rounded to two decimals, is **3.83%**. Now let's explore the flair of this financial sector! Treasury bills have a fascinating history—they were introduced during the Great Depression as a way for the government to manage its cash needs efficiently. Over the years, they've become a safe haven for investors seeking stability, often flocked to during market volatility. If you're intrigued by T-bills, there’s plenty more ahead! Consider reading about the nuances of government securities and how they play into macroeconomic strategies, or dive deep into the intriguing world of interest rates and their impact on investment decisions. It’s a rabbit hole worth exploring!