Question

Treasury Securities.

Consider a 4-year semiannual TIPS with a coupon rate of 6%. Suppose that an investor purchases $1,000,000 of par value (initial principal) of this issue today, and that the annual inflation rate is 2.8% for the 1st six-month period and 3.2% for the 2nd six month period. What is the dollar coupon interest that will be paid in cash at the end of the 2nd six-month period?

Suppose the quote on a bank discount for a treasury bill with 90 days to maturity and a face value of $1,000 is 5% what is the price?

Answer 1

Calculating Dollar coupon interest paid in cash at end of 2nd six month period for TIPS

Par value = $1000000, Coupon rate = 6%

Semi annual coupon rate = Coupon rate / 2 = 6% / 2 = 3%

Semi annual annual for first six months = Annual inflation for 1st six months = 2.8% / 2 = 1.4%

Inflation adjusted principal at end of first six months = Par value x (1+ Semi annual annual for first six months) = 1000000 x (1+1.4%) = 1000000 x 1.014 = 1014000

Semi annual inflation for 2nd six months = Annual inflation for 2nd six months / 2 = 3.2% / 2 = 1.6%

Inflation adjusted principal at end of 2nd six months = Inflation adjusted principal at end of first six months x (Semi annual inflation for 2nd six months) = 1014000 x (1+1.6%) = 1014000 x 1.016 = 1030224

Dollar coupon interest paid at end of 2nd six month = Inflation adjusted principal at end of 2nd six months x Semi annual coupon rate = 1030224 x 3% = 30906.72

Hence Dollar coupon interest paid at end of 2nd six month = 30906.72

Calculating Price of Treasury bill

Face value = $1000, Days to maturity = t = 90, Bank discount yield = 5%

Bank discount yield = (Discount / Face value)(360/t)

5% = (Discount / 1000)(360/90)

5% = (Discount / 1000)(4)

Discount =( 5% x 1000) / 4 = 12.50

Price of T bill = Face value - discount = 1000 - 12.50 = $987.50

Hence Price of T bill = $987.50