Question

Suppose a ten-year, $ 1 000 bond with an 8.4 % coupon rate and semi-annual coupons is trading for a price of $ 1 035.72. a. What is the bond's yield to maturity (expressed as an APR with semi-annual compounding)? b. If the bond's yield to maturity changes to 9.1 % APR , what will the bond's price be?

a. The bond's yield to maturity is

nothing %.

(Enter your response as a percent rounded to two decimal places.)

b. The new price for the bond is

$nothing.

(Round to the nearest cent.)

Answer 1

a)semiannual interest = 1000*.084*6/12 = 42

semiannual months = 10*2 =20

Yield to maturity = [Interest +(face value -issue price)/months ][(face value +price)/2]

       =[42+(1000-1035.72)/20]/[(1000+1035.72)/2]

         =[42 + (-35.72/20)]/[2035.72 /2]

       = [42 - 1.786]/1017.86

         = 40.214/1017.86

      = 3.94%

Annual yield to maturity = 3.94 *2 = 7.88%

b)semiannual yield =9.1*6/12= 4.55%

price =[PVA4.55%,20*Interest ]+[PVF4.5%,20*Face value]

     =[12.95176*42]+[.41069*1000]

      = 543.97+ 410.69

     = 954.66