Question

1a.) What is the price of a T-bill that matures in 270 days if the discount rate is 0.9% and par is $1,000?

1b.) What is the yield on a T-bill maturing in 180 days with a $990 current price and a $1000 par value?

Please show work and original formulas

Answer 1

1a.) What is the price of a T-bill that matures in 270 days if the discount rate is 0.9% and par is $1,000?

{(Par value of T-bills – Price of T-bill)/ Price of T-bill} * {number of days in a year/days remaining in maturity) = Yield or discount rate of T-bill

Where,

Par value of T-bill = $1000

Price of T-bill P =?

Number of days in a year = 365 days

Days remaining in maturity = 270 days

Yield or discount rate of T-bill = 0.9%

Therefore,

{($1000 –P)/P} * (365/270) = 0.9%

Or P = $993.37

1b.) What is the yield on a T-bill maturing in 180 days with a $990 current price and a $1000 par value?

{(Par value of T-bills – Price of T-bill)/ Price of T-bill} * {number of days in a year/days remaining in maturity) = Yield or discount rate of T-bill

Where,

Par value of T-bill = $1000

Price of T-bill P =990

Number of days in a year = 365 days

Days remaining in maturity = 180 days

Yield or discount rate of T-bill, i =?

Therefore,

{($1000 –990)/990} * (365/180) = i

Or i = 0.02048 or 2.048%

Therefore yield on a T-bill is 2.048%.