What is the coupon rate of a bond that is currently selling

What is the coupon rate of a bond that is currently selling for $1100, matures in 15 years, pays the coupons monthly and the current market rate is 8.2%?

Solution

We need to find the Monthly Coupon Payment =PMT

Value of Bond = PV of PMT + PV of MaturityValue

PV factor for Coupon Payament= (1-(1+8.2%/12)^(-15*12))/(8.2%/12)=103.3876

PV factor fo Matruity value = (1/(1+8.2%/12))^(15*12)=.29351

Value of Bond = PV of PMT + PV of MaturityValue

1100=103.3876*PMT + .29351*1000

PMT =7.80057

Hence Coupon Rate =7.80057/1000*12 =9.36%

Alternate Method using EXcel PMT funtion

Rate =8.2%/12

NPER =15*12

PV =1100

FV =1000

PMT=PMT(8.2%/12,15*12,-1100,1000)

PMT =7.80057

Hence Coupon Rate =7.80057/1000*12 =9.36%