Question

Suppose you buy a 30 year bond that pays a 6% coupon for the first 15 years and a 8% coupon for the last 15 years. The YTM of this bond is 7%. What is the price of the bond?

（please provide formula）

Answer 1

Calculation of price of the bond 15 years from now :

FV = 1000
Nper = 15
PMT = 1000 * 8% = 80
Rate = 7%

Price can be calculated by using the following excel formula:
=PV(rate,nper,pmt,fv)
=PV(7%,15,-80,-1000)
= $1,091.08

Calculation of price of the bond today:

Nper = 15
Rate = 7%
PMT = 1000 * 6% = 60
FV = $1,091.08

Price can be calculated by using the following excel formula:
=PV(rate,nper,pmt,fv)
=PV(7%,15,-60,-1091.08)
= $941.93

Price of the bond = $941.93