Question

Today is 15-Feb-2018 Table 13.2 2 T-Bond Quotations Maturity Coupon Bid Asked Chg Ask Yld 8/15/20 8.875 116.3135 Calculate-0.21881.921 2/15/41 2.375 98.5156 98.5781-1.1016 2.398 4

Calculate the capital income, B_t, for the 2/15/41 T-Bond using the information provided in the bond quotations in Table 13.2 above. Continue to assume a $5,000 par value.

a) Assume today is 15-Feb-2018, B_t = $

b) Assume today is 15-Feb-2041, B_t = $

Answer 1

For 2/15/41 bond, coupon rate = 2.375%

Assume semi annual coupon payments

Part (a)

Rate = yield per period = semi annual yield = Ask yiled / 2 = 2.398% / 2 = 1.199%

Period = nos. of half years in time left to maturity = 2 x (2041 - 2018) = 46

PMT = payment per period = semi annual coupon = 2.375% / 2 x Par value = 1.18750% x $ 5,000 =  59.38

FV = Future Value = Par value = 5,000

Hence, B_t = price of the bonds today = - PV (Rate, Period, PMT, FV) = - PV (1.199%, 46, 59.38, 5000) =  $4,979.76

Part (b)

Assume today is 15-Feb-2041 = maturity date

On maturity date, price of the bond is pulled to par.

Hence, B_t = Par value = $ 5,000