Question

what annual interest rate is earned by a 27 week t bill with a maturity value of 30000 that sells for 26542

Answer 1

Here, we are required to calculate the annual interest rate earned by a 27week t bill with a maturity value of 30000 that sells for 26542.

The annual interest rate earned by a 27 week t bill with a maturity value of 30000 that sells for 26542 is 5.475%

First, it is important to evaluate the settlement price per $1 of the maturity value. This is denoted by the symbol p.

• Therefore, according to this question, the settlement price per $1 of the maturity value is p:
• and p = 26542/30000 = 0.884733.

• Also, it's important to evaluate the number of days to maturity which is the difference between the maturity date and the age of the t bill. denoted by Nsm
• The age of the t bill is 27 weeks = 189 days.
• Therefore, Nsm = 360 - 189 = 171 days.

Therefore, the annual interest rate of the t bill, denoted by d is:

d = (1 - p) × {Nsb/360} × 100%.

Therefore, d = (1 - 0.884733) × {171/360} = 5.475%

Consequently, the annual interest rate earned by a 27 week t bill with a maturity value of 30000 that sells for 26542 is 5.475%.

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