Question

You purchase a 182 day T-bill when it is issued.  The bill has a par value of $1,000, and you paid $990 for it.

1. What is the T-bill discount when you purchased the bill?

2. What is the T-bill yield expected to be if you hold the bill until maturity?

3. If you hold the bill for 60 days and sell it in the secondary market for $995, what is the T-bill yield on your investment?

Answer 1

1. What is the T-bill discount when you purchased the bill?

Treasury bills are among the safest investments in the market. They're backed by the full faith and credit of the U.S. government, and they come in maturities ranging from four weeks to one year.

Here, 182 day T-bill purchased, has a par value of $1,000, and $990 paid for it. So, T-bill discount when purchased = $1000 - $990 = $10

The Treasury-bill doesn't make separate interest payments on Treasury bills. Instead, the discounted price accounts for the interest that you'll earn. In this case, you'll receive $1,000 at the end of the 182-day period. Because you only paid $990, the remaining $10 represents the interest on your investment over that time frame.

2.What is the T-bill yield expected to be if you hold the bill until maturity?

The imputed interest rate on a T-bill. As discussed earlier, T-bills are issued at a discount off their $1,000 par value, not quoted as a yield. To determine that yield, you need to know the price and the number of days to maturity. For simplicity's sake, a year is considered to be 360 days long, which assumes there are 30 days in a month. (This day-count convention may actually make things more complicated, but the 360-day year is now a tradition for calculating T-bill rates).

Computing a T-bill's discount yield is a three-step process. For these purposes, carry all computations out to six digits to the right of the decimal point.

Step#1          Subtract the price you paid for the bond from $1,000. Take the difference and divide it by 1,000.

Here, the buying price of the bond is $990. Subtract $990 from $1,000 and divide the resulting $10 by 1,000, and you end up with $0.01.

Step#2          Now you take 360 - the number of days in a year, by convention - and divide that by the days to maturity. It is a 182 bill. Now divide 360 days by 182 days for a result of 1.978022

Step#3          Now you multiply the result of step 1 by that of step 2. $0.01 times 1.978022 equals 0.0197 or 1.97%

3.If you hold the bill for 60 days and sell it in the secondary market for $995, what is the T-bill yield on your investment?

YT = (SP – PP/PP)(360 / n)

        Y_T = {(995- 990)/ 990] * (360/60) *100

        Y_T = 0.00505 * 6 *100

        Y_T = 3.03%