Final answer:
The student needs to calculate both the purchase price of a $100,000 182-days T-Bill with a 5% yield and the simple interest rate earned when sold 80 days before maturity. Calculations are based on financial formulas for discounted price and simple interest rate, though the exact answers require numerical calculations that are not provided here.
Step-by-step explanation:
The student is asking two questions about financial mathematics related to Treasury Bills (T-Bills). First, they want to calculate the price Rycroft Philostrate paid for a $100,000 182-days T-Bill yielding a 5% rate of return. This involves identifying the discounted price of the T-Bill. Second, they want to calculate the simple interest rate that Rycroft got when he sold the T-Bill for $98,702 80 days before maturity.
To calculate the purchase price of the T-Bill, we use the formula: Price = Face Value / (1 + (Yield x (Days to Maturity/360)))
where the face value is $100,000, the annual yield is 5%, and the days to maturity are 182. The exact calculations would require this formula, but we don't have the workings shown here to get the exact value.
Then, to calculate the simple interest rate that Rycroft got from the investment, we can use the formula:
Simple Interest Rate = ((Selling Price - Purchase Price) / Purchase Price) x (360 / Holding Period)
Here the selling price is $98,702, the purchase price would be the calculated value from the first step, and the holding period is 182 - 80 = 102 days. Again, calculations would follow these steps but are not shown in entirety. Note that the exact answer for a) and b) can't be provided without performing the actual calculations, which are based on formulas similar to those outlined above.