A Treasury bill with 131 days to maturity is quoted at 96.920. What is the bank
ID: 2771924 • Letter: A
Question
A Treasury bill with 131 days to maturity is quoted at 96.920. What is the bank discount yield, the bond equivalent yield, and the effective annual return? (Do not round intermediate calculations. Enter your answers as a percent rounded to 3 decimal places. Omit the "%" sign in your response.)
A Treasury bill with 131 days to maturity is quoted at 96.920. What is the bank discount yield, the bond equivalent yield, and the effective annual return? (Do not round intermediate calculations. Enter your answers as a percent rounded to 3 decimal places. Omit the "%" sign in your response.)
Explanation / Answer
1.Discount Yield
Discount Yield is a measure of a bond’s percentage return.Discount yield is most frequently used to calculate the yield on short term bonds and treasury bills sold at a discount.This yield calculation uses a 30-day month and 360-day year to simplify calculations.
Discount yield is calculated by the following formula:
DISCOUNT YIELD=[(par value - purchase price)/par value] * [360/days to maturity]
=[(100 - 96.92)/100] * [360/131]=0.08464
2.Bond Equivalent Yield
A calculation for restating semi-annual,quarterly, or monthly discount-bond or note yields into an annual yield.For a fixed income security with a par value of $1000,the calculation is as follows:
Bond Equivalent Yield= [(1000- purchase price)/Purchase price] * [365/days to maturity]
=0.088543
3.Effective annual return
The effective annual interest rate is the rate of interest an investor earns in a year after accounting for the effects of compounding.
How it works/Example:
The formula for effective annual interest rate is:
(1 + i / n)n - 1
Where
i= the stated annual interest rate
n=the number of compounding periods in one year
Using the discount rate as the annual rate of interest,i.e. 8.46 ,we will calculate the effective annual return as
=(1 + .08/8)8 - 1 = 1.05459=10.54%
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