Question

In November 2017, Treasury 4 1/2s of 2044 offered a semiannually compounded yield to maturity of 2.66%. Recognizing that coupons are paid semiannually, calculate the bond's price. Assume face value is $1,000. (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Answer 1

The bond price is $1352.82.   
or periods = time to x frequency of Given;- a) coupon rate - 4.5% 6 Time to maturity = (2044-2017) = 274rs. c) Frequency of payment semiannually =2 times d) total no of periods = time to x e maturity = 27 X 2 = 54 payment e) coupon rate per period = 4.5/2 = 2.25% f . coupon value = Face value x coupon rate Per period = $ 1000 X 2:25). - $ 22.5 9 ytm = 2.66% h) ytm per period - 2.66/2 = 1.33% Calculation of Bond price. By using the formula Bond = Coupon per period + coupon per period price [+ gield perperiod) Tit gield per period)" -.-.t couponper period t maturity value [it yield per perica)st (it yield per periods By substituting values into the equation we have - Bond = 22.5 +22.5 t...+22.5 Price (1+0.0133)' (1+0.0133) 2 (1+0.013354 1000 (H0.013354 P.T.O

it follows a Geometr a Geometrical progression (GP) with first term = 22.5 & common - 1.0133 1.0133 No of terms = 54 n. using Gp formula = 1st term x 11-/common ratio) (1-common ratio) . Good = 22.5 x 11- (1/1.0133) + 1000 Price 1.0133 1.0133 (1.0133) 54 - 862 88 + 489.94 = 1352.82 Notes :- 1) I have used GP formula to calculate Coupon Payments because it will be cumbersome to use of calculate bond price formula as the no of Periods are large pe upto 54 terms. 2) ytm & yield are used interchangeably in my above calculations 3) Bond price is the sum total of PV of all cashflows (coupon paymets & maturity proceeds) of each period at ytm per period.