On January 18, 2007 BusinessWeek reported yields on Treasury bills. Bruce Martin purchased a $10,000 13-week Treasury bill at $9,881.25. (a) What was the amount of interest? (b) What was the effective reate of interest?
1.56
To calculate the amount of interest on a Treasury bill, we need to know the face value (purchase price) of the bill and the discount price at which it was bought. In this case, the face value of the Treasury bill is $10,000, and it was purchased at a discount price of $9,881.25.
(a) To find the amount of interest, we subtract the purchase price from the face value:
Amount of interest = Face value - Purchase price
Amount of interest = $10,000 - $9,881.25 = $118.75
Therefore, the amount of interest on the Treasury bill is $118.75.
(b) The effective rate of interest is the annualized rate of return earned on the Treasury bill. As the Treasury bill has a maturity period of 13 weeks (or approximately 91 days), we need to convert the amount of interest into an annual rate.
To do this, we'll use the formula for Effective Annual Yield (EAY):
EAY = ((1 + i/n)^(n*m))-1
where i is the interest rate per compounding period, n is the number of compounding periods in a year, and m is the number of years.
In this case, there are 52 weeks in a year, and since the Treasury bill has a 13-week maturity, we have:
i = (Amount of interest / Purchase price) = ($118.75 / $9,881.25) = 0.012
Now, let's calculate the effective annual yield:
EAY = ((1 + 0.012/4)^(4*13/52)) - 1
EAY = ((1 + 0.003)^(1.0)) - 1
EAY = (1.003)^1 - 1
EAY = 0.003
Therefore, the effective annual yield, or the effective rate of interest, on this Treasury bill is 0.3% or 0.003 as a decimal.