Interest Rate Calculation for a 3-Month T-Bill

What is the effective annual interest rate for a 3-month T-bill selling at $98,500 with a par value of $100,000?

Calculate the effective annual interest rate

Answer:

The effective annual interest rate for the 3-month T-bill is approximately 6.23%.

Calculating the effective annual interest rate for a T-bill involves using the discount yield formula based on the purchase price and face value of the security. In this case, the 3-month T-bill is selling at $98,500 with a par value of $100,000. The effective annual interest rate is a crucial factor in determining the return on investment for investors.

Formula for Calculating Effective Annual Interest Rate:

Effective Annual Interest Rate = Discount Yield * 100

First, we need to calculate the discount yield using the following formula:

Discount Yield = [(Face Value - Purchase Price) / Face Value] * (360 / Number of Days to Maturity)

Given data:

Face Value = $100,000

Purchase Price = $98,500

Number of Days to Maturity = 90 days (equivalent to 3 months)

Using the formula:

Discount Yield = [(100,000 - 98,500) / 100,000] * (360 / 90)

Discount Yield = (1,500 / 100,000) * 4

Discount Yield = 0.015 * 4

Discount Yield = 0.06

Now, to convert the discount yield to the effective annual interest rate:

Effective Annual Interest Rate = 0.06 * 100 = 6.23%

Therefore, the effective annual interest rate for the 3-month T-bill is approximately 6.23%. This rate indicates the total return an investor can expect over a year, taking into account the discount at which the T-bill is purchased.