Problem 1: Assume A 1000 Treasury Bill Quoted To Pay 5

Problem 1assume That A 1000 Treasury Bill Is Quoted To Pay 5 Interes

Assume that a $1000 treasury bill is quoted to pay 5% interest over a six-month period. How much interest would the investor receive? What will be the price of the treasury bill? What will be the effective yield?

Paper For Above instruction

The problem involves calculating the interest received, the price of the treasury bill, and its effective yield based on a quoted interest rate over a six-month period. Treasury bills (T-bills) are sold at a discount and do not pay periodic interest; instead, the interest is the difference between the purchase price and the face value at maturity. Therefore, the given interest rate of 5% over six months indicates the discount rate for the T-bill.

First, we determine the discount amount. Since the T-bill has a face value of $1000 and the interest is 5% over six months, the interest (or discount) can be calculated as:

Interest (discount) = Face Value × Discount Rate = $1000 × 0.05 = $50

However, because T-bills are sold at a discount, the purchase price is:

Price = Face Value - Discount = $1000 - $50 = $950

Therefore, the investor pays $950 and receives $1000 at maturity. The interest received by the investor is the difference between face value and purchase price, which is $50.

To determine the effective yield (annualized yield), considering the six-month period, we use the following formula:

Effective Yield = (Interest / Purchase Price) × (Number of periods in a year)

Since interest is for six months, there are 2 periods in a year:

Effective Yield = ($50 / $950) × 2 ≈ 0.05263 × 2 ≈ 0.10526 or 10.526%

This indicates that the annualized effective yield of the T-bill is approximately 10.53%. This yield accounts for the discount rate implied by the quoted interest over six months.

Summary of Calculations:

  • Interest received for six months: $50
  • Price of the T-bill: $950
  • Effective annual yield: approximately 10.53%

References

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