Introduction

In the realm of financial markets, the ability to convert discount rates into corresponding prices is a fundamental skill. This chapter delves into the process of converting a discount rate to a price for a US Treasury bill. US Treasury bills, often referred to as T-bills, are short-term debt securities issued by the US government. Understanding how to calculate the price of a T-bill from its discount rate is crucial for investors and financial professionals who engage in trading these instruments.

Understanding Discount Rates and Prices

Before we dive into the calculations, let’s clarify the concepts of discount rates and prices. A discount rate represents the rate at which future cash flows are discounted back to their present value. It reflects the opportunity cost of tying up funds in an investment. On the other hand, the price of a financial instrument, such as a T-bill, is the amount an investor is willing to pay for the right to receive the instrument’s future cash flows.

Calculation of T-Bill Price from Discount Rate

The formula to calculate the price (P) of a US Treasury bill based on its discount rate (D) is given by:

$$P=\frac{F}{1-D \times \frac{T}{360}}$$ Where:

• $F$ is the face value of the T-bill
• $D$ is the discount rate expressed as a decimal
• $T$ is the number of days to maturity

Example: Let’s consider a US Treasury bill with a face value of USD 10,000$, a discount rate of 0.025 (or USD 2.5 %), and 60 days to maturity.

Using the formula: $$P=\frac{10000}{1-0.025 \times \frac{60}{350}}=\frac{10000}{0.98333} \approx 10168.73$$ Therefore, the price of the US Treasury bill is approximately USD 10,168.73.

Sensitivity to Discount Rate

It’s important to note that the price of a T-bill is inversely related to the discount rate. As the discount rate increases, the price of the T-bill decreases, and vice versa. This relationship reflects the concept that higher discount rates result in higher present value discounts, leading to lower prices.