Question

A U.S. Treasury bill with 56 days to maturity is quoted at a discount yield of 1.20 percent. Assume a $1 million face value. What is the bond equivalent yield? (Do not round intermediate calculations. Enter your answer as a percent rounded to 3 decimal places.) Bond equivalent yield 18.400 % 3 decimal places

Answer 1

Compute the purchase price of T-bill, using the equation as shown below:

Discount yield = {(Face value – Purchase price)/ Face value}*365 days/ Days in maturity

             1.20% = {($1,000,000 – Purchase price)/ $1,000,000}*365 days/ 56 days

After rearranging the above-metioned equation, the purchase price comes out to be:

Purchase price = $1,000,000 - (1.20%*56 days*$1,000,000/365 days)

                         = $1,000,000 – 18,410.09589041

                         = $998,158.90411

Hence, the purchase price of the T-bill is $998,158.90411.

Compute the bond equivalent bond, using the equation as shown below:

Bond yield = {(Face value – Purchase price)/ Purchase price}*365 days/ Days in maturity

                   = {($1,000,000 – $998,158.90411)/ $998,158.90411}*365 days/ 56

                  = 1.202%

Hence, the equivalent bond yield is 1.202%.