Question

A t-bill with face value $10,000 and 87 days to maturity is selling at a bank discount ask yield of 3.4%.

Answer 1

Answer:

a. The price of a T-bill with a Face value of $10,000, maturing in 87 days at 3.4% annual yield of interest is $9917.83.

b. It's Bond equivalent yield (BEY) is 3.48%.

a. We follow these steps to arrive at the answer.

Since T-bills are like zero-coupon bonds,the price paid for them will be less than the Face Value. The difference between the face value and the purchase price is the interest earned for the period.

First, we calculate the daily interest rate factor. We do that by using the following formula:

$Daily interest rate factor = \frac{(Interest rate * Days to maturity)}{360}$

Substituting the values from the question in the formula above, we get,

$Daily interest rate factor = \frac{0.034*87}{360}$

$Daily interest rate factor = \{2.958}{360}$

$Daily interest rate factor = 0.008216667$

Next, we subtract the daily interest rate factor from 1.

$1 - 0.008216667 = 0.991783333$

Finally, we multiply the answer above with the face value of the T-bill to arrive at the purchase price.

$Purchase Price of T-bill = 10,000 * 0.991783333$

$Purchase Price = 9917.83$

b.

The Bond Equivalent Yield  or BEY helps in calculating the annual yield of bonds that are sold at discount (i.e. those bonds that don't have interest payments).

We can calculate the bond equivalent yield as follows:

$BEY = \frac{Face Value - purchase price}{purchase price} * \frac{365}{no. of days}$

Substituting the values above in the formula we get,

$BEY = \frac{10000-9917.833333}{9917.833333} *\frac{365}{87}$

$BEY = 0.00828474 * 4.195402299$

BEY = 0.034757816  or 3.48%