Question

Assume an investor purchased a three-month t-bill with a $10,000 par value for $9,500 and sold it 45 days later for $9,600. what is the yield?

Answer 1

The yield on a Treasury bill can be calculated using the formula for discount yield:

\[ \text{Discount Yield} = \left( \frac{\text{Face Value} - \text{Purchase Price}}{\text{Face Value}} \right) \times \left( \frac{\text{Number of Days in a Year}}{\text{Number of Days to Maturity}} \right) \]

In this case, the face value is $10,000, the purchase price is $9,500, and the bill was held for 45 days.

\[ \text{Discount Yield} = \left( \frac{10,000 - 9,500}{10,000} \right) \times \left( \frac{365}{45} \right) \]

\[ \text{Discount Yield} = 0.05 \times 8.11 \]

\[ \text{Discount Yield} \approx 0.4055 \]

To express this as a percentage, multiply by 100:

\[ \text{Discount Yield} \approx 40.55\% \]

Therefore, the yield on the three-month T-bill is approximately 40.55%.

Answer 2

The yield on the T-bill is 1.05%.

Step-by-step explanation:

When interest rates rise, bonds previously issued at lower interest rates will sell for less than face value. Conversely, when interest rates fall, bonds previously issued at higher interest rates will sell for more than face value.

In this case, the investor purchased a three-month T-bill with a $10,000 par value for $9,500 and sold it 45 days later for $9,600. To calculate the yield, we can use the formula:

Yield = (Final Value - Purchase Price) / Purchase Price

Substituting the given values, the yield is:

Yield = ($9,600 - $9,500) / $9,500 = 1.05%

So, the yield on the T-bill is 1.05%.