Question

What is the price of a 33​-year, 7.9 % coupon​ rate, $1,000 face value bond that pays interest quarterly if the yield to maturity on similar bonds is 11.9%​?

Answer 1

Since, the payment is paid quarterly

No. of periods = 33*4 = 132 periods

Quarterly YTM = 11.9%/4 = 2.975%

Face value of the bond = 1000

Annual coupon rate = 7.9%, therefore, quarterly coupon rate = 7.9%/4 = 1.975%

Quartely coupon Payment = 1.975%*1000 = $19.75

Following are the cashflows till 132nd period:

C(1) =C(2) =.....=C(131) = 19.75 and C(132)= 1019.75

The formula to calculate the present value of bond is given by below equation:

PV = 670.8787321

We can also use Financial calculator(BA II Plus)

N =132, I/Y = 2.975, PMT = 19.75, FV=1000 CPT --> PV = 670.8787321

Answer -> $670.8787321