Ninety-one-day Treasury bills carry an investment return (IR) of 6.25 percent. What is their purchase price? What is their discount rate (DR)?

What are the formulas and how do you figure the answer?

Thank you so very much.

To determine the purchase price and discount rate of the 91-day Treasury bills, we need to use the formulas for these calculations.

1. Purchase Price (PP):
The formula to calculate the purchase price of a Treasury bill is:
PP = Face Value / (1 + (IR × Days)/365)

Where:
- PP represents the purchase price,
- Face Value denotes the face value of the bill (which is usually $1,000 for Treasury bills),
- IR represents the investment return (6.25% expressed as 0.0625), and
- Days represents the number of days until maturity (which is 91 for a 91-day Treasury bill).

Substituting these values into the formula, we can calculate the purchase price (PP) as follows:
PP = 1000 / (1 + (0.0625 × 91)/365)
PP ≈ 1000 / (1 + 0.015625)
PP ≈ 1000 / 1.015625
PP ≈ 984.375

Therefore, the purchase price of the 91-day Treasury bill is approximately $984.375.

2. Discount Rate (DR):
The discount rate represents the difference between the face value and the purchase price, expressed as a percentage of the face value. The formula to calculate the discount rate is:
DR = (Face Value - PP) / Face Value

Using the calculated value for the purchase price (PP) of $984.375 and the face value (FV) of $1,000, we can compute the discount rate (DR) as follows:
DR = (1000 - 984.375) / 1000
DR ≈ 0.015625

Therefore, the discount rate of the 91-day Treasury bill is approximately 1.5625%.